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2017


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Robot Learning

Peters, J., Lee, D., Kober, J., Nguyen-Tuong, D., Bagnell, J., Schaal, S.

In Springer Handbook of Robotics, pages: 357-394, 15, 2nd, (Editors: Siciliano, Bruno and Khatib, Oussama), Springer International Publishing, 2017 (inbook)

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Project Page [BibTex]

2017


Project Page [BibTex]

2013


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Learning and Optimization with Submodular Functions

Sankaran, B., Ghazvininejad, M., He, X., Kale, D., Cohen, L.

ArXiv, May 2013 (techreport)

Abstract
In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it is beneficial to have strong guarantees on the tractable approximate solutions. In order operate under these criterion most optimization problems are cast under the umbrella of convexity or submodularity. In this report we will study design and optimization over a common class of functions called submodular functions. Set functions, and specifically submodular set functions, characterize a wide variety of naturally occurring optimization problems, and the property of submodularity of set functions has deep theoretical consequences with wide ranging applications. Informally, the property of submodularity of set functions concerns the intuitive principle of diminishing returns. This property states that adding an element to a smaller set has more value than adding it to a larger set. Common examples of submodular monotone functions are entropies, concave functions of cardinality, and matroid rank functions; non-monotone examples include graph cuts, network flows, and mutual information. In this paper we will review the formal definition of submodularity; the optimization of submodular functions, both maximization and minimization; and finally discuss some applications in relation to learning and reasoning using submodular functions.

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arxiv link (url) [BibTex]

2013


arxiv link (url) [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]