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2016


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Structured contact force optimization for kino-dynamic motion generation

Herzog, A., Schaal, S., Righetti, L.

In 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages: 2703-2710, IEEE, Daejeon, South Korea, 2016 (inproceedings)

Abstract
Optimal control approaches in combination with trajectory optimization have recently proven to be a promising control strategy for legged robots. Computationally efficient and robust algorithms were derived using simplified models of the contact interaction between robot and environment such as the linear inverted pendulum model (LIPM). However, as humanoid robots enter more complex environments, less restrictive models become increasingly important. As we leave the regime of linear models, we need to build dedicated solvers that can compute interaction forces together with consistent kinematic plans for the whole-body. In this paper, we address the problem of planning robot motion and interaction forces for legged robots given predefined contact surfaces. The motion generation process is decomposed into two alternating parts computing force and motion plans in coherence. We focus on the properties of the momentum computation leading to sparse optimal control formulations to be exploited by a dedicated solver. In our experiments, we demonstrate that our motion generation algorithm computes consistent contact forces and joint trajectories for our humanoid robot. We also demonstrate the favorable time complexity due to our formulation and composition of the momentum equations.

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link (url) DOI [BibTex]

2016


link (url) DOI [BibTex]


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Balancing and Walking Using Full Dynamics LQR Control With Contact Constraints

Mason, S., Rotella, N., Schaal, S., Righetti, L.

In 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids), pages: 63-68, IEEE, Cancun, Mexico, 2016 (inproceedings)

Abstract
Torque control algorithms which consider robot dynamics and contact constraints are important for creating dynamic behaviors for humanoids. As computational power increases, algorithms tend to also increase in complexity. However, it is not clear how much complexity is really required to create controllers which exhibit good performance. In this paper, we study the capabilities of a simple approach based on contact consistent LQR controllers designed around key poses to control various tasks on a humanoid robot. We present extensive experimental results on a hydraulic, torque controlled humanoid performing balancing and stepping tasks. This feedback control approach captures the necessary synergies between the DoFs of the robot to guarantee good control performance. We show that for the considered tasks, it is only necessary to re-linearize the dynamics of the robot at different contact configurations and that increasing the number of LQR controllers along desired trajectories does not improve performance. Our result suggest that very simple controllers can yield good performance competitive with current state of the art, but more complex, optimization-based whole-body controllers. A video of the experiments can be found at https://youtu.be/5T08CNKV1hw.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Step Timing Adjustement: a Step toward Generating Robust Gaits

Khadiv, M., Herzog, A., Moosavian, S. A. A., Righetti, L.

In 2016 IEEE-RAS 16th International Conference on Humanoid Robots (Humanoids), pages: 35-42, IEEE, Cancun, Mexico, 2016 (inproceedings)

Abstract
Step adjustment for humanoid robots has been shown to improve robustness in gaits. However, step duration adaptation is often neglected in control strategies. In this paper, we propose an approach that combines both step location and timing adjustment for generating robust gaits. In this approach, step location and step timing are decided, based on feedback from the current state of the robot. The proposed approach is comprised of two stages. In the first stage, the nominal step location and step duration for the next step or a previewed number of steps are specified. In this stage which is done at the start of each step, the main goal is to specify the best step length and step duration for a desired walking speed. The second stage deals with finding the best landing point and landing time of the swing foot at each control cycle. In this stage, stability of the gaits is preserved by specifying a desired offset between the swing foot landing point and the Divergent Component of Motion (DCM) at the end of current step. After specifying the landing point of the swing foot at a desired time, the swing foot trajectory is regenerated at each control cycle to realize desired landing properties. Simulation on different scenarios shows the robustness of the generated gaits from our proposed approach compared to the case where no timing adjustment is employed.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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On the Effects of Measurement Uncertainty in Optimal Control of Contact Interactions

Ponton, B., Schaal, S., Righetti, L.

In The 12th International Workshop on the Algorithmic Foundations of Robotics WAFR, Berkeley, USA, 2016 (inproceedings)

Abstract
Stochastic Optimal Control (SOC) typically considers noise only in the process model, i.e. unknown disturbances. However, in many robotic applications involving interaction with the environment, such as locomotion and manipulation, uncertainty also comes from lack of precise knowledge of the world, which is not an actual disturbance. We analyze the effects of also considering noise in the measurement model, by devel- oping a SOC algorithm based on risk-sensitive control, that includes the dynamics of an observer in such a way that the control law explicitly de- pends on the current measurement uncertainty. In simulation results on a simple 2D manipulator, we have observed that measurement uncertainty leads to low impedance behaviors, a result in contrast with the effects of process noise that creates stiff behaviors. This suggests that taking into account measurement uncertainty could be a potentially very interesting way to approach problems involving uncertain contact interactions.

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link (url) [BibTex]

link (url) [BibTex]


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A Convex Model of Momentum Dynamics for Multi-Contact Motion Generation

Ponton, B., Herzog, A., Schaal, S., Righetti, L.

In 2016 IEEE-RAS 16th International Conference on Humanoid Robots Humanoids, pages: 842-849, IEEE, Cancun, Mexico, 2016 (inproceedings)

Abstract
Linear models for control and motion generation of humanoid robots have received significant attention in the past years, not only due to their well known theoretical guarantees, but also because of practical computational advantages. However, to tackle more challenging tasks and scenarios such as locomotion on uneven terrain, a more expressive model is required. In this paper, we are interested in contact interaction-centered motion optimization based on the momentum dynamics model. This model is non-linear and non-convex; however, we find a relaxation of the problem that allows us to formulate it as a single convex quadratically-constrained quadratic program (QCQP) that can be very efficiently optimized and is useful for multi-contact planning. This convex model is then coupled to the optimization of end-effector contact locations using a mixed integer program, which can also be efficiently solved. This becomes relevant e.g. to recover from external pushes, where a predefined stepping plan is likely to fail and an online adaptation of the contact location is needed. The performance of our algorithm is demonstrated in several multi-contact scenarios for a humanoid robot.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]

2015


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Distributed Event-based State Estimation

Trimpe, S.

Max Planck Institute for Intelligent Systems, November 2015 (techreport)

Abstract
An event-based state estimation approach for reducing communication in a networked control system is proposed. Multiple distributed sensor-actuator-agents observe a dynamic process and sporadically exchange their measurements and inputs over a bus network. Based on these data, each agent estimates the full state of the dynamic system, which may exhibit arbitrary inter-agent couplings. Local event-based protocols ensure that data is transmitted only when necessary to meet a desired estimation accuracy. This event-based scheme is shown to mimic a centralized Luenberger observer design up to guaranteed bounds, and stability is proven in the sense of bounded estimation errors for bounded disturbances. The stability result extends to the distributed control system that results when the local state estimates are used for distributed feedback control. Simulation results highlight the benefit of the event-based approach over classical periodic ones in reducing communication requirements.

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arXiv [BibTex]

2015


arXiv [BibTex]


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Automatic LQR Tuning Based on Gaussian Process Optimization: Early Experimental Results

Marco, A., Hennig, P., Bohg, J., Schaal, S., Trimpe, S.

Machine Learning in Planning and Control of Robot Motion Workshop at the IEEE/RSJ International Conference on Intelligent Robots and Systems (iROS), pages: , , Machine Learning in Planning and Control of Robot Motion Workshop, October 2015 (conference)

Abstract
This paper proposes an automatic controller tuning framework based on linear optimal control combined with Bayesian optimization. With this framework, an initial set of controller gains is automatically improved according to a pre-defined performance objective evaluated from experimental data. The underlying Bayesian optimization algorithm is Entropy Search, which represents the latent objective as a Gaussian process and constructs an explicit belief over the location of the objective minimum. This is used to maximize the information gain from each experimental evaluation. Thus, this framework shall yield improved controllers with fewer evaluations compared to alternative approaches. A seven-degree-of-freedom robot arm balancing an inverted pole is used as the experimental demonstrator. Preliminary results of a low-dimensional tuning problem highlight the method’s potential for automatic controller tuning on robotic platforms.

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PDF DOI Project Page [BibTex]

PDF DOI Project Page [BibTex]


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Gaussian Process Optimization for Self-Tuning Control

Marco, A.

Polytechnic University of Catalonia (BarcelonaTech), October 2015 (mastersthesis)

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PDF Project Page [BibTex]

PDF Project Page [BibTex]


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Adaptive and Learning Concepts in Hydraulic Force Control

Doerr, A.

University of Stuttgart, September 2015 (mastersthesis)

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[BibTex]

[BibTex]


Thumb xl screen shot 2015 08 22 at 21.47.37
Direct Loss Minimization Inverse Optimal Control

Doerr, A., Ratliff, N., Bohg, J., Toussaint, M., Schaal, S.

In Proceedings of Robotics: Science and Systems, Rome, Italy, Robotics: Science and Systems XI, July 2015 (inproceedings)

Abstract
Inverse Optimal Control (IOC) has strongly impacted the systems engineering process, enabling automated planner tuning through straightforward and intuitive demonstration. The most successful and established applications, though, have been in lower dimensional problems such as navigation planning where exact optimal planning or control is feasible. In higher dimensional systems, such as humanoid robots, research has made substantial progress toward generalizing the ideas to model free or locally optimal settings, but these systems are complicated to the point where demonstration itself can be difficult. Typically, real-world applications are restricted to at best noisy or even partial or incomplete demonstrations that prove cumbersome in existing frameworks. This work derives a very flexible method of IOC based on a form of Structured Prediction known as Direct Loss Minimization. The resulting algorithm is essentially Policy Search on a reward function that rewards similarity to demonstrated behavior (using Covariance Matrix Adaptation (CMA) in our experiments). Our framework blurs the distinction between IOC, other forms of Imitation Learning, and Reinforcement Learning, enabling us to derive simple, versatile, and practical algorithms that blend imitation and reinforcement signals into a unified framework. Our experiments analyze various aspects of its performance and demonstrate its efficacy on conveying preferences for motion shaping and combined reach and grasp quality optimization.

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PDF Video Project Page [BibTex]

PDF Video Project Page [BibTex]


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LMI-Based Synthesis for Distributed Event-Based State Estimation

Muehlebach, M., Trimpe, S.

In Proceedings of the American Control Conference, July 2015 (inproceedings)

Abstract
This paper presents an LMI-based synthesis procedure for distributed event-based state estimation. Multiple agents observe and control a dynamic process by sporadically exchanging data over a broadcast network according to an event-based protocol. In previous work [1], the synthesis of event-based state estimators is based on a centralized design. In that case three different types of communication are required: event-based communication of measurements, periodic reset of all estimates to their joint average, and communication of inputs. The proposed synthesis problem eliminates the communication of inputs as well as the periodic resets (under favorable circumstances) by accounting explicitly for the distributed structure of the control system.

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PDF DOI Project Page [BibTex]

PDF DOI Project Page [BibTex]


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Guaranteed H2 Performance in Distributed Event-Based State Estimation

Muehlebach, M., Trimpe, S.

In Proceeding of the First International Conference on Event-based Control, Communication, and Signal Processing, June 2015 (inproceedings)

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PDF DOI Project Page [BibTex]

PDF DOI Project Page [BibTex]


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On the Choice of the Event Trigger in Event-based Estimation

Trimpe, S., Campi, M.

In Proceeding of the First International Conference on Event-based Control, Communication, and Signal Processing, June 2015 (inproceedings)

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PDF DOI Project Page [BibTex]

PDF DOI Project Page [BibTex]


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Event-based Estimation and Control for Remote Robot Operation with Reduced Communication

Trimpe, S., Buchli, J.

In Proceedings of the IEEE International Conference on Robotics and Automation, May 2015 (inproceedings)

Abstract
An event-based communication framework for remote operation of a robot via a bandwidth-limited network is proposed. The robot sends state and environment estimation data to the operator, and the operator transmits updated control commands or policies to the robot. Event-based communication protocols are designed to ensure that data is transmitted only when required: the robot sends new estimation data only if this yields a significant information gain at the operator, and the operator transmits an updated control policy only if this comes with a significant improvement in control performance. The developed framework is modular and can be used with any standard estimation and control algorithms. Simulation results of a robotic arm highlight its potential for an efficient use of limited communication resources, for example, in disaster response scenarios such as the DARPA Robotics Challenge.

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PDF DOI Project Page [BibTex]

PDF DOI Project Page [BibTex]


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Lernende Roboter

Trimpe, S.

In Jahrbuch der Max-Planck-Gesellschaft, Max Planck Society, May 2015, (popular science article in German) (inbook)

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link (url) [BibTex]

link (url) [BibTex]


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Policy Search for Imitation Learning

Doerr, A.

University of Stuttgart, January 2015 (thesis)

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link (url) Project Page [BibTex]

link (url) Project Page [BibTex]


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A New Perspective and Extension of the Gaussian Filter

Wüthrich, M., Trimpe, S., Kappler, D., Schaal, S.

In Robotics: Science and Systems, 2015 (inproceedings)

Abstract
The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. GFs represent the belief of the current state by a Gaussian with the mean being an affine function of the measurement. We show that this representation can be too restrictive to accurately capture the dependencies in systems with nonlinear observation models, and we investigate how the GF can be generalized to alleviate this problem. To this end we view the GF from a variational-inference perspective, and analyze how restrictions on the form of the belief can be relaxed while maintaining simplicity and efficiency. This analysis provides a basis for generalizations of the GF. We propose one such generalization which coincides with a GF using a virtual measurement, obtained by applying a nonlinear function to the actual measurement. Numerical experiments show that the proposed Feature Gaussian Filter (FGF) can have a substantial performance advantage over the standard GF for systems with nonlinear observation models.

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Web PDF Project Page [BibTex]


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Kinematic and gait similarities between crawling human infants and other quadruped mammals

Righetti, L., Nylen, A., Rosander, K., Ijspeert, A.

Frontiers in Neurology, 6(17), February 2015 (article)

Abstract
Crawling on hands and knees is an early pattern of human infant locomotion, which offers an interesting way of studying quadrupedalism in one of its simplest form. We investigate how crawling human infants compare to other quadruped mammals, especially primates. We present quantitative data on both the gait and kinematics of seven 10-month-old crawling infants. Body movements were measured with an optoelectronic system giving precise data on 3-dimensional limb movements. Crawling on hands and knees is very similar to the locomotion of non-human primates in terms of the quite protracted arm at touch-down, the coordination between the spine movements in the lateral plane and the limbs, the relatively extended limbs during locomotion and the strong correlation between stance duration and speed of locomotion. However, there are important differences compared to primates, such as the choice of a lateral-sequence walking gait, which is similar to most non-primate mammals and the relatively stiff elbows during stance as opposed to the quite compliant gaits of primates. These finding raise the question of the role of both the mechanical structure of the body and neural control on the determination of these characteristics.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Trajectory generation for multi-contact momentum control

Herzog, A., Rotella, N., Schaal, S., Righetti, L.

In 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids), pages: 874-880, IEEE, Seoul, South Korea, 2015 (inproceedings)

Abstract
Simplified models of the dynamics such as the linear inverted pendulum model (LIPM) have proven to perform well for biped walking on flat ground. However, for more complex tasks the assumptions of these models can become limiting. For example, the LIPM does not allow for the control of contact forces independently, is limited to co-planar contacts and assumes that the angular momentum is zero. In this paper, we propose to use the full momentum equations of a humanoid robot in a trajectory optimization framework to plan its center of mass, linear and angular momentum trajectories. The model also allows for planning desired contact forces for each end-effector in arbitrary contact locations. We extend our previous results on linear quadratic regulator (LQR) design for momentum control by computing the (linearized) optimal momentum feedback law in a receding horizon fashion. The resulting desired momentum and the associated feedback law are then used in a hierarchical whole body control approach. Simulation experiments show that the approach is computationally fast and is able to generate plans for locomotion on complex terrains while demonstrating good tracking performance for the full humanoid control.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Humanoid Momentum Estimation Using Sensed Contact Wrenches

Rotella, N., Herzog, A., Schaal, S., Righetti, L.

In 2015 IEEE-RAS 15th International Conference on Humanoid Robots (Humanoids), pages: 556-563, IEEE, Seoul, South Korea, 2015 (inproceedings)

Abstract
This work presents approaches for the estimation of quantities important for the control of the momentum of a humanoid robot. In contrast to previous approaches which use simplified models such as the Linear Inverted Pendulum Model, we present estimators based on the momentum dynamics of the robot. By using this simple yet dynamically-consistent model, we avoid the issues of using simplified models for estimation. We develop an estimator for the center of mass and full momentum which can be reformulated to estimate center of mass offsets as well as external wrenches applied to the robot. The observability of these estimators is investigated and their performance is evaluated in comparison to previous approaches.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]

2014


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Wenn es was zu sagen gibt

(Klaus Tschira Award 2014 in Computer Science)

Trimpe, S.

Bild der Wissenschaft, pages: 20-23, November 2014, (popular science article in German) (article)

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PDF Project Page [BibTex]

2014


PDF Project Page [BibTex]


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A Self-Tuning LQR Approach Demonstrated on an Inverted Pendulum

Trimpe, S., Millane, A., Doessegger, S., D’Andrea, R.

In Proceedings of the 19th IFAC World Congress, Cape Town, South Africa, 2014 (inproceedings)

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PDF Supplementary material DOI [BibTex]

PDF Supplementary material DOI [BibTex]


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A Limiting Property of the Matrix Exponential

Trimpe, S., D’Andrea, R.

IEEE Transactions on Automatic Control, 59(4):1105-1110, 2014 (article)

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PDF DOI [BibTex]

PDF DOI [BibTex]


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Event-Based State Estimation With Variance-Based Triggering

Trimpe, S., D’Andrea, R.

IEEE Transactions on Automatic Control, 59(12):3266-3281, 2014 (article)

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PDF Supplementary material DOI Project Page [BibTex]

PDF Supplementary material DOI Project Page [BibTex]


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Stability Analysis of Distributed Event-Based State Estimation

Trimpe, S.

In Proceedings of the 53rd IEEE Conference on Decision and Control, Los Angeles, CA, 2014 (inproceedings)

Abstract
An approach for distributed and event-based state estimation that was proposed in previous work [1] is analyzed and extended to practical networked systems in this paper. Multiple sensor-actuator-agents observe a dynamic process, sporadically exchange their measurements over a broadcast network according to an event-based protocol, and estimate the process state from the received data. The event-based approach was shown in [1] to mimic a centralized Luenberger observer up to guaranteed bounds, under the assumption of identical estimates on all agents. This assumption, however, is unrealistic (it is violated by a single packet drop or slight numerical inaccuracy) and removed herein. By means of a simulation example, it is shown that non-identical estimates can actually destabilize the overall system. To achieve stability, the event-based communication scheme is supplemented by periodic (but infrequent) exchange of the agentsâ?? estimates and reset to their joint average. When the local estimates are used for feedback control, the stability guarantee for the estimation problem extends to the event-based control system.

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PDF Supplementary material DOI Project Page [BibTex]

PDF Supplementary material DOI Project Page [BibTex]


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Dual Execution of Optimized Contact Interaction Trajectories

Toussaint, M., Ratliff, N., Bohg, J., Righetti, L., Englert, P., Schaal, S.

In 2014 IEEE/RSJ Conference on Intelligent Robots and Systems, pages: 47-54, IEEE, Chicago, USA, 2014 (inproceedings)

Abstract
Efficient manipulation requires contact to reduce uncertainty. The manipulation literature refers to this as funneling: a methodology for increasing reliability and robustness by leveraging haptic feedback and control of environmental interaction. However, there is a fundamental gap between traditional approaches to trajectory optimization and this concept of robustness by funneling: traditional trajectory optimizers do not discover force feedback strategies. From a POMDP perspective, these behaviors could be regarded as explicit observation actions planned to sufficiently reduce uncertainty thereby enabling a task. While we are sympathetic to the full POMDP view, solving full continuous-space POMDPs in high-dimensions is hard. In this paper, we propose an alternative approach in which trajectory optimization objectives are augmented with new terms that reward uncertainty reduction through contacts, explicitly promoting funneling. This augmentation shifts the responsibility of robustness toward the actual execution of the optimized trajectories. Directly tracing trajectories through configuration space would lose all robustness-dual execution achieves robustness by devising force controllers to reproduce the temporal interaction profile encoded in the dual solution of the optimization problem. This work introduces dual execution in depth and analyze its performance through robustness experiments in both simulation and on a real-world robotic platform.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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An autonomous manipulation system based on force control and optimization

Righetti, L., Kalakrishnan, M., Pastor, P., Binney, J., Kelly, J., Voorhies, R. C., Sukhatme, G. S., Schaal, S.

Autonomous Robots, 36(1-2):11-30, January 2014 (article)

Abstract
In this paper we present an architecture for autonomous manipulation. Our approach is based on the belief that contact interactions during manipulation should be exploited to improve dexterity and that optimizing motion plans is useful to create more robust and repeatable manipulation behaviors. We therefore propose an architecture where state of the art force/torque control and optimization-based motion planning are the core components of the system. We give a detailed description of the modules that constitute the complete system and discuss the challenges inherent to creating such a system. We present experimental results for several grasping and manipulation tasks to demonstrate the performance and robustness of our approach.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Learning of grasp selection based on shape-templates

Herzog, A., Pastor, P., Kalakrishnan, M., Righetti, L., Bohg, J., Asfour, T., Schaal, S.

Autonomous Robots, 36(1-2):51-65, January 2014 (article)

Abstract
The ability to grasp unknown objects still remains an unsolved problem in the robotics community. One of the challenges is to choose an appropriate grasp configuration, i.e., the 6D pose of the hand relative to the object and its finger configuration. In this paper, we introduce an algorithm that is based on the assumption that similarly shaped objects can be grasped in a similar way. It is able to synthesize good grasp poses for unknown objects by finding the best matching object shape templates associated with previously demonstrated grasps. The grasp selection algorithm is able to improve over time by using the information of previous grasp attempts to adapt the ranking of the templates to new situations. We tested our approach on two different platforms, the Willow Garage PR2 and the Barrett WAM robot, which have very different hand kinematics. Furthermore, we compared our algorithm with other grasp planners and demonstrated its superior performance. The results presented in this paper show that the algorithm is able to find good grasp configurations for a large set of unknown objects from a relatively small set of demonstrations, and does improve its performance over time.

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link (url) DOI [BibTex]


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Balancing experiments on a torque-controlled humanoid with hierarchical inverse dynamics

Herzog, A., Righetti, L., Grimminger, F., Pastor, P., Schaal, S.

In 2014 IEEE/RSJ Conference on Intelligent Robots and Systems, pages: 981-988, IEEE, Chicago, USA, 2014 (inproceedings)

Abstract
Recently several hierarchical inverse dynamics controllers based on cascades of quadratic programs have been proposed for application on torque controlled robots. They have important theoretical benefits but have never been implemented on a torque controlled robot where model inaccuracies and real-time computation requirements can be problematic. In this contribution we present an experimental evaluation of these algorithms in the context of balance control for a humanoid robot. The presented experiments demonstrate the applicability of the approach under real robot conditions (i.e. model uncertainty, estimation errors, etc). We propose a simplification of the optimization problem that allows us to decrease computation time enough to implement it in a fast torque control loop. We implement a momentum-based balance controller which shows robust performance in face of unknown disturbances, even when the robot is standing on only one foot. In a second experiment, a tracking task is evaluated to demonstrate the performance of the controller with more complicated hierarchies. Our results show that hierarchical inverse dynamics controllers can be used for feedback control of humanoid robots and that momentum-based balance control can be efficiently implemented on a real robot.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Full Dynamics LQR Control of a Humanoid Robot: An Experimental Study on Balancing and Squatting

Mason, S., Righetti, L., Schaal, S.

In 2014 IEEE-RAS International Conference on Humanoid Robots, pages: 374-379, IEEE, Madrid, Spain, 2014 (inproceedings)

Abstract
Humanoid robots operating in human environments require whole-body controllers that can offer precise tracking and well-defined disturbance rejection behavior. In this contribution, we propose an experimental evaluation of a linear quadratic regulator (LQR) using a linearization of the full robot dynamics together with the contact constraints. The advantage of the controller is that it explicitly takes into account the coupling between the different joints to create optimal feedback controllers for whole-body control. We also propose a method to explicitly regulate other tasks of interest, such as the regulation of the center of mass of the robot or its angular momentum. In order to evaluate the performance of linear optimal control designs in a real-world scenario (model uncertainty, sensor noise, imperfect state estimation, etc), we test the controllers in a variety of tracking and balancing experiments on a torque controlled humanoid (e.g. balancing, split plane balancing, squatting, pushes while squatting, and balancing on a wheeled platform). The proposed control framework shows a reliable push recovery behavior competitive with more sophisticated balance controllers, rejecting impulses up to 11.7 Ns with peak forces of 650 N, with the added advantage of great computational simplicity. Furthermore, the controller is able to track squatting trajectories up to 1 Hz without relinearization, suggesting that the linearized dynamics is sufficient for significant ranges of motion.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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State Estimation for a Humanoid Robot

Rotella, N., Bloesch, M., Righetti, L., Schaal, S.

In 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 952-958, IEEE, Chicago, USA, 2014 (inproceedings)

Abstract
This paper introduces a framework for state estimation on a humanoid robot platform using only common proprioceptive sensors and knowledge of leg kinematics. The presented approach extends that detailed in prior work on a point-foot quadruped platform by adding the rotational constraints imposed by the humanoid's flat feet. As in previous work, the proposed Extended Kalman Filter accommodates contact switching and makes no assumptions about gait or terrain, making it applicable on any humanoid platform for use in any task. A nonlinear observability analysis is performed on both the point-foot and flat-foot filters and it is concluded that the addition of rotational constraints significantly simplifies singular cases and improves the observability characteristics of the system. Results on a simulated walking dataset demonstrate the performance gain of the flat-foot filter as well as confirm the results of the presented observability analysis.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]

2013


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AGILITY – Dynamic Full Body Locomotion and Manipulation with Autonomous Legged Robots

Hutter, M., Bloesch, M., Buchli, J., Semini, C., Bazeille, S., Righetti, L., Bohg, J.

In 2013 IEEE International Symposium on Safety, Security, and Rescue Robotics (SSRR), pages: 1-4, IEEE, Linköping, Sweden, 2013 (inproceedings)

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link (url) DOI [BibTex]

2013


link (url) DOI [BibTex]


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Learning Objective Functions for Manipulation

Kalakrishnan, M., Pastor, P., Righetti, L., Schaal, S.

In 2013 IEEE International Conference on Robotics and Automation, IEEE, Karlsruhe, Germany, 2013 (inproceedings)

Abstract
We present an approach to learning objective functions for robotic manipulation based on inverse reinforcement learning. Our path integral inverse reinforcement learning algorithm can deal with high-dimensional continuous state-action spaces, and only requires local optimality of demonstrated trajectories. We use L 1 regularization in order to achieve feature selection, and propose an efficient algorithm to minimize the resulting convex objective function. We demonstrate our approach by applying it to two core problems in robotic manipulation. First, we learn a cost function for redundancy resolution in inverse kinematics. Second, we use our method to learn a cost function over trajectories, which is then used in optimization-based motion planning for grasping and manipulation tasks. Experimental results show that our method outperforms previous algorithms in high-dimensional settings.

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link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Using Torque Redundancy to Optimize Contact Forces in Legged Robots

Righetti, L., Buchli, J., Mistry, M., Kalakrishnan, M., Schaal, S.

In Redundancy in Robot Manipulators and Multi-Robot Systems, 57, pages: 35-51, Lecture Notes in Electrical Engineering, Springer Berlin Heidelberg, 2013 (incollection)

Abstract
The development of legged robots for complex environments requires controllers that guarantee both high tracking performance and compliance with the environment. More specifically the control of contact interaction with the environment is of crucial importance to ensure stable, robust and safe motions. In the following, we present an inverse dynamics controller that exploits torque redundancy to directly and explicitly minimize any combination of linear and quadratic costs in the contact constraints and in the commands. Such a result is particularly relevant for legged robots as it allows to use torque redundancy to directly optimize contact interactions. For example, given a desired locomotion behavior, it can guarantee the minimization of contact forces to reduce slipping on difficult terrains while ensuring high tracking performance of the desired motion. The proposed controller is very simple and computationally efficient, and most importantly it can greatly improve the performance of legged locomotion on difficult terrains as can be seen in the experimental results.

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link (url) [BibTex]

link (url) [BibTex]


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Optimal distribution of contact forces with inverse-dynamics control

Righetti, L., Buchli, J., Mistry, M., Kalakrishnan, M., Schaal, S.

The International Journal of Robotics Research, 32(3):280-298, March 2013 (article)

Abstract
The development of legged robots for complex environments requires controllers that guarantee both high tracking performance and compliance with the environment. More specifically the control of the contact interaction with the environment is of crucial importance to ensure stable, robust and safe motions. In this contribution we develop an inverse-dynamics controller for floating-base robots under contact constraints that can minimize any combination of linear and quadratic costs in the contact constraints and the commands. Our main result is the exact analytical derivation of the controller. Such a result is particularly relevant for legged robots as it allows us to use torque redundancy to directly optimize contact interactions. For example, given a desired locomotion behavior, we can guarantee the minimization of contact forces to reduce slipping on difficult terrains while ensuring high tracking performance of the desired motion. The main advantages of the controller are its simplicity, computational efficiency and robustness to model inaccuracies. We present detailed experimental results on simulated humanoid and quadruped robots as well as a real quadruped robot. The experiments demonstrate that the controller can greatly improve the robustness of locomotion of the robots.1

am mg

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Controlled Reduction with Unactuated Cyclic Variables: Application to 3D Bipedal Walking with Passive Yaw Rotation

Gregg, R., Righetti, L.

IEEE Transactions on Automatic Control, 58(10):2679-2685, October 2013 (article)

Abstract
This technical note shows that viscous damping can shape momentum conservation laws in a manner that stabilizes yaw rotation and enables steering for underactuated 3D walking. We first show that unactuated cyclic variables can be controlled by passively shaped conservation laws given a stabilizing controller in the actuated coordinates. We then exploit this result to realize controlled geometric reduction with multiple unactuated cyclic variables. We apply this underactuated control strategy to a five-link 3D biped to produce exponentially stable straight-ahead walking and steering in the presence of passive yawing.

mg

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Learning Task Error Models for Manipulation

Pastor, P., Kalakrishnan, M., Binney, J., Kelly, J., Righetti, L., Sukhatme, G. S., Schaal, S.

In 2013 IEEE Conference on Robotics and Automation, IEEE, Karlsruhe, Germany, 2013 (inproceedings)

Abstract
Precise kinematic forward models are important for robots to successfully perform dexterous grasping and manipulation tasks, especially when visual servoing is rendered infeasible due to occlusions. A lot of research has been conducted to estimate geometric and non-geometric parameters of kinematic chains to minimize reconstruction errors. However, kinematic chains can include non-linearities, e.g. due to cable stretch and motor-side encoders, that result in significantly different errors for different parts of the state space. Previous work either does not consider such non-linearities or proposes to estimate non-geometric parameters of carefully engineered models that are robot specific. We propose a data-driven approach that learns task error models that account for such unmodeled non-linearities. We argue that in the context of grasping and manipulation, it is sufficient to achieve high accuracy in the task relevant state space. We identify this relevant state space using previously executed joint configurations and learn error corrections for those. Therefore, our system is developed to generate subsequent executions that are similar to previous ones. The experiments show that our method successfully captures the non-linearities in the head kinematic chain (due to a counterbalancing spring) and the arm kinematic chains (due to cable stretch) of the considered experimental platform, see Fig. 1. The feasibility of the presented error learning approach has also been evaluated in independent DARPA ARM-S testing contributing to successfully complete 67 out of 72 grasping and manipulation tasks.

am mg

link (url) DOI [BibTex]

link (url) DOI [BibTex]

2012


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Encoding of Periodic and their Transient Motions by a Single Dynamic Movement Primitive

Ernesti, J., Righetti, L., Do, M., Asfour, T., Schaal, S.

In 2012 12th IEEE-RAS International Conference on Humanoid Robots (Humanoids 2012), pages: 57-64, IEEE, Osaka, Japan, November 2012 (inproceedings)

am mg

link (url) DOI [BibTex]

2012


link (url) DOI [BibTex]


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Learning Force Control Policies for Compliant Robotic Manipulation

Kalakrishnan, M., Righetti, L., Pastor, P., Schaal, S.

In ICML’12 Proceedings of the 29th International Coference on International Conference on Machine Learning, pages: 49-50, Edinburgh, Scotland, 2012 (inproceedings)

am mg

[BibTex]

[BibTex]


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Quadratic programming for inverse dynamics with optimal distribution of contact forces

Righetti, L., Schaal, S.

In 2012 12th IEEE-RAS International Conference on Humanoid Robots (Humanoids 2012), pages: 538-543, IEEE, Osaka, Japan, November 2012 (inproceedings)

Abstract
In this contribution we propose an inverse dynamics controller for a humanoid robot that exploits torque redundancy to minimize any combination of linear and quadratic costs in the contact forces and the commands. In addition the controller satisfies linear equality and inequality constraints in the contact forces and the commands such as torque limits, unilateral contacts or friction cones limits. The originality of our approach resides in the formulation of the problem as a quadratic program where we only need to solve for the control commands and where the contact forces are optimized implicitly. Furthermore, we do not need a structured representation of the dynamics of the robot (i.e. an explicit computation of the inertia matrix). It is in contrast with existing methods based on quadratic programs. The controller is then robust to uncertainty in the estimation of the dynamics model and the optimization is fast enough to be implemented in high bandwidth torque control loops that are increasingly available on humanoid platforms. We demonstrate properties of our controller with simulations of a human size humanoid robot.

am mg

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Towards Associative Skill Memories

Pastor, P., Kalakrishnan, M., Righetti, L., Schaal, S.

In 2012 12th IEEE-RAS International Conference on Humanoid Robots (Humanoids 2012), pages: 309-315, IEEE, Osaka, Japan, November 2012 (inproceedings)

Abstract
Movement primitives as basis of movement planning and control have become a popular topic in recent years. The key idea of movement primitives is that a rather small set of stereotypical movements should suffice to create a large set of complex manipulation skills. An interesting side effect of stereotypical movement is that it also creates stereotypical sensory events, e.g., in terms of kinesthetic variables, haptic variables, or, if processed appropriately, visual variables. Thus, a movement primitive executed towards a particular object in the environment will associate a large number of sensory variables that are typical for this manipulation skill. These association can be used to increase robustness towards perturbations, and they also allow failure detection and switching towards other behaviors. We call such movement primitives augmented with sensory associations Associative Skill Memories (ASM). This paper addresses how ASMs can be acquired by imitation learning and how they can create robust manipulation skill by determining subsequent ASMs online to achieve a particular manipulation goal. Evaluation for grasping and manipulation with a Barrett WAM/Hand illustrate our approach.

am mg

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Template-based learning of grasp selection

Herzog, A., Pastor, P., Kalakrishnan, M., Righetti, L., Asfour, T., Schaal, S.

In 2012 IEEE International Conference on Robotics and Automation, pages: 2379-2384, IEEE, Saint Paul, USA, 2012 (inproceedings)

Abstract
The ability to grasp unknown objects is an important skill for personal robots, which has been addressed by many present and past research projects, but still remains an open problem. A crucial aspect of grasping is choosing an appropriate grasp configuration, i.e. the 6d pose of the hand relative to the object and its finger configuration. Finding feasible grasp configurations for novel objects, however, is challenging because of the huge variety in shape and size of these objects. Moreover, possible configurations also depend on the specific kinematics of the robotic arm and hand in use. In this paper, we introduce a new grasp selection algorithm able to find object grasp poses based on previously demonstrated grasps. Assuming that objects with similar shapes can be grasped in a similar way, we associate to each demonstrated grasp a grasp template. The template is a local shape descriptor for a possible grasp pose and is constructed using 3d information from depth sensors. For each new object to grasp, the algorithm then finds the best grasp candidate in the library of templates. The grasp selection is also able to improve over time using the information of previous grasp attempts to adapt the ranking of the templates. We tested the algorithm on two different platforms, the Willow Garage PR2 and the Barrett WAM arm which have very different hands. Our results show that the algorithm is able to find good grasp configurations for a large set of objects from a relatively small set of demonstrations, and does indeed improve its performance over time.

am mg

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Probabilistic depth image registration incorporating nonvisual information

Wüthrich, M., Pastor, P., Righetti, L., Billard, A., Schaal, S.

In 2012 IEEE International Conference on Robotics and Automation, pages: 3637-3644, IEEE, Saint Paul, USA, 2012 (inproceedings)

Abstract
In this paper, we derive a probabilistic registration algorithm for object modeling and tracking. In many robotics applications, such as manipulation tasks, nonvisual information about the movement of the object is available, which we will combine with the visual information. Furthermore we do not only consider observations of the object, but we also take space into account which has been observed to not be part of the object. Furthermore we are computing a posterior distribution over the relative alignment and not a point estimate as typically done in for example Iterative Closest Point (ICP). To our knowledge no existing algorithm meets these three conditions and we thus derive a novel registration algorithm in a Bayesian framework. Experimental results suggest that the proposed methods perform favorably in comparison to PCL [1] implementations of feature mapping and ICP, especially if nonvisual information is available.

am mg

link (url) DOI [BibTex]

link (url) DOI [BibTex]

2011


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Toward simple control for complex, autonomous robotic applications: combining discrete and rhythmic motor primitives

Degallier, S., Righetti, L., Gay, S., Ijspeert, A.

Autonomous Robots, 31(2-3):155-181, October 2011 (article)

Abstract
Vertebrates are able to quickly adapt to new environments in a very robust, seemingly effortless way. To explain both this adaptivity and robustness, a very promising perspective in neurosciences is the modular approach to movement generation: Movements results from combinations of a finite set of stable motor primitives organized at the spinal level. In this article we apply this concept of modular generation of movements to the control of robots with a high number of degrees of freedom, an issue that is challenging notably because planning complex, multidimensional trajectories in time-varying environments is a laborious and costly process. We thus propose to decrease the complexity of the planning phase through the use of a combination of discrete and rhythmic motor primitives, leading to the decoupling of the planning phase (i.e. the choice of behavior) and the actual trajectory generation. Such implementation eases the control of, and the switch between, different behaviors by reducing the dimensionality of the high-level commands. Moreover, since the motor primitives are generated by dynamical systems, the trajectories can be smoothly modulated, either by high-level commands to change the current behavior or by sensory feedback information to adapt to environmental constraints. In order to show the generality of our approach, we apply the framework to interactive drumming and infant crawling in a humanoid robot. These experiments illustrate the simplicity of the control architecture in terms of planning, the integration of different types of feedback (vision and contact) and the capacity of autonomously switching between different behaviors (crawling and simple reaching).

mg

link (url) DOI [BibTex]

2011


link (url) DOI [BibTex]


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Learning Force Control Policies for Compliant Manipulation

Kalakrishnan, M., Righetti, L., Pastor, P., Schaal, S.

In 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 4639-4644, IEEE, San Francisco, USA, sep 2011 (inproceedings)

Abstract
Developing robots capable of fine manipulation skills is of major importance in order to build truly assistive robots. These robots need to be compliant in their actuation and control in order to operate safely in human environments. Manipulation tasks imply complex contact interactions with the external world, and involve reasoning about the forces and torques to be applied. Planning under contact conditions is usually impractical due to computational complexity, and a lack of precise dynamics models of the environment. We present an approach to acquiring manipulation skills on compliant robots through reinforcement learning. The initial position control policy for manipulation is initialized through kinesthetic demonstration. We augment this policy with a force/torque profile to be controlled in combination with the position trajectories. We use the Policy Improvement with Path Integrals (PI2) algorithm to learn these force/torque profiles by optimizing a cost function that measures task success. We demonstrate our approach on the Barrett WAM robot arm equipped with a 6-DOF force/torque sensor on two different manipulation tasks: opening a door with a lever door handle, and picking up a pen off the table. We show that the learnt force control policies allow successful, robust execution of the tasks.

am mg

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Control of legged robots with optimal distribution of contact forces

Righetti, L., Buchli, J., Mistry, M., Schaal, S.

In 2011 11th IEEE-RAS International Conference on Humanoid Robots, pages: 318-324, IEEE, Bled, Slovenia, 2011 (inproceedings)

Abstract
The development of agile and safe humanoid robots require controllers that guarantee both high tracking performance and compliance with the environment. More specifically, the control of contact interaction is of crucial importance for robots that will actively interact with their environment. Model-based controllers such as inverse dynamics or operational space control are very appealing as they offer both high tracking performance and compliance. However, while widely used for fully actuated systems such as manipulators, they are not yet standard controllers for legged robots such as humanoids. Indeed such robots are fundamentally different from manipulators as they are underactuated due to their floating-base and subject to switching contact constraints. In this paper we present an inverse dynamics controller for legged robots that use torque redundancy to create an optimal distribution of contact constraints. The resulting controller is able to minimize, given a desired motion, any quadratic cost of the contact constraints at each instant of time. In particular we show how this can be used to minimize tangential forces during locomotion, therefore significantly improving the locomotion of legged robots on difficult terrains. In addition to the theoretical result, we present simulations of a humanoid and a quadruped robot, as well as experiments on a real quadruped robot that demonstrate the advantages of the controller.

am mg

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Learning Motion Primitive Goals for Robust Manipulation

Stulp, F., Theodorou, E., Kalakrishnan, M., Pastor, P., Righetti, L., Schaal, S.

In IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 325-331, IEEE, San Francisco, USA, sep 2011 (inproceedings)

Abstract
Applying model-free reinforcement learning to manipulation remains challenging for several reasons. First, manipulation involves physical contact, which causes discontinuous cost functions. Second, in manipulation, the end-point of the movement must be chosen carefully, as it represents a grasp which must be adapted to the pose and shape of the object. Finally, there is uncertainty in the object pose, and even the most carefully planned movement may fail if the object is not at the expected position. To address these challenges we 1) present a simplified, computationally more efficient version of our model-free reinforcement learning algorithm PI2; 2) extend PI2 so that it simultaneously learns shape parameters and goal parameters of motion primitives; 3) use shape and goal learning to acquire motion primitives that are robust to object pose uncertainty. We evaluate these contributions on a manipulation platform consisting of a 7-DOF arm with a 4-DOF hand.

am mg

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Inverse Dynamics Control of Floating-Base Robots with External Constraints: a Unified View

Righetti, L., Buchli, J., Mistry, M., Schaal, S.

In 2011 IEEE International Conference on Robotics and Automation, pages: 1085-1090, IEEE, Shanghai, China, 2011 (inproceedings)

Abstract
Inverse dynamics controllers and operational space controllers have proved to be very efficient for compliant control of fully actuated robots such as fixed base manipulators. However legged robots such as humanoids are inherently different as they are underactuated and subject to switching external contact constraints. Recently several methods have been proposed to create inverse dynamics controllers and operational space controllers for these robots. In an attempt to compare these different approaches, we develop a general framework for inverse dynamics control and show that these methods lead to very similar controllers. We are then able to greatly simplify recent whole-body controllers based on operational space approaches using kinematic projections, bringing them closer to efficient practical implementations. We also generalize these controllers such that they can be optimal under an arbitrary quadratic cost in the commands.

am mg

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Operational Space Control of Constrained and Underactuated Systems

Mistry, M., Righetti, L.

In Proceedings of Robotics: Science and Systems, Los Angeles, CA, USA, June 2011 (inproceedings)

Abstract
The operational space formulation (Khatib, 1987), applied to rigid-body manipulators, describes how to decouple task-space and null-space dynamics, and write control equations that correspond only to forces at the end-effector or, alternatively, only to motion within the null-space. We would like to apply this useful theory to modern humanoids and other legged systems, for manipulation or similar tasks, however these systems present additional challenges due to their underactuated floating bases and contact states that can dynamically change. In recent work, Sentis et al. derived controllers for such systems by implementing a task Jacobian projected into a space consistent with the supporting constraints and underactuation (the so called "support consistent reduced Jacobian"). Here, we take a new approach to derive operational space controllers for constrained underactuated systems, by first considering the operational space dynamics within "projected inverse-dynamics" (Aghili, 2005), and subsequently resolving underactuation through the addition of dynamically consistent control torques. Doing so results in a simplified control solution compared with previous results, and importantly yields several new insights into the underlying problem of operational space control in constrained environments: 1) Underactuated systems, such as humanoid robots, cannot in general completely decouple task and null-space dynamics. However, 2) there may exist an infinite number of control solutions to realize desired task-space dynamics, and 3) these solutions involve the addition of dynamically consistent null-space motion or constraint forces (or combinations of both). In light of these findings, we present several possible control solutions, with varying optimization criteria, and highlight some of their practical consequences.

mg

link (url) DOI [BibTex]

link (url) DOI [BibTex]


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Online movement adaptation based on previous sensor experiences

Pastor, P., Righetti, L., Kalakrishnan, M., Schaal, S.

In 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages: 365-371, IEEE, San Francisco, USA, sep 2011 (inproceedings)

Abstract
Personal robots can only become widespread if they are capable of safely operating among humans. In uncertain and highly dynamic environments such as human households, robots need to be able to instantly adapt their behavior to unforseen events. In this paper, we propose a general framework to achieve very contact-reactive motions for robotic grasping and manipulation. Associating stereotypical movements to particular tasks enables our system to use previous sensor experiences as a predictive model for subsequent task executions. We use dynamical systems, named Dynamic Movement Primitives (DMPs), to learn goal-directed behaviors from demonstration. We exploit their dynamic properties by coupling them with the measured and predicted sensor traces. This feedback loop allows for online adaptation of the movement plan. Our system can create a rich set of possible motions that account for external perturbations and perception uncertainty to generate truly robust behaviors. As an example, we present an application to grasping with the WAM robot arm.

am mg

link (url) DOI [BibTex]

link (url) DOI [BibTex]