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Smooth Approximations for Hybrid Optimal Control Problems with Application to Robotic Walking

Westenbroek, Tyler and Xiong, Xiaobin and Sastry, S. Shankar and Ames, Aaron D. (2021) Smooth Approximations for Hybrid Optimal Control Problems with Application to Robotic Walking. IFAC-PapersOnLine, 54 (5). pp. 181-186. ISSN 2405-8963. doi:10.1016/j.ifacol.2021.08.495.

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This paper investigates optimal control problems formulated over a class of hybrid dynamical systems which display event-triggered discrete jumps. Due to the discontinuous nature of the underlying dynamics, previous approaches to solving optimal control problems over this class of systems generally rely on fixing the number and sequence of discrete jumps a priori, or search over possible mode sequences in a combinatorial manner. Employing contributions from the geometric theory of hybrid systems, we instead formulate a family of smooth approximate problems formulated over a family of smooth control systems which faithfully approximate the dynamics of the original hybrid system, in an appropriate metric. Efficient gradient-based methods can be used to solve the smooth approximations, without specifying the sequence of discrete transitions ahead of time. Under appropriate hypothesis, the gradients of the smooth problem are shown to be well-conditioned and closely approximate the gradients of the non-smooth problem (when they exist). Two cases studies demonstrate the utility of the approach, including an in-depth application to generating a stable walking motion for a bipedal robot.

Item Type:Article
Related URLs:
URLURL TypeDescription
Westenbroek, Tyler0000-0003-1111-3118
Xiong, Xiaobin0000-0002-6275-3900
Ames, Aaron D.0000-0003-0848-3177
Additional Information:© 2021 The Authors. This is an open access article under the CC BY-NC-ND license ( Available online 9 September 2021. Peer review under responsibility of International Federation of Automatic Control.
Issue or Number:5
Record Number:CaltechAUTHORS:20220104-157181000
Persistent URL:
Official Citation:Tyler Westenbroek, Xiaobin Xiong, S Shankar Sastry, Aaron D. Ames, Smooth Approximations for Hybrid Optimal Control Problems with Application to Robotic Walking, IFAC-PapersOnLine, Volume 54, Issue 5, 2021, Pages 181-186, ISSN 2405-8963,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:112675
Deposited By: George Porter
Deposited On:04 Jan 2022 23:37
Last Modified:04 Jan 2022 23:37

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