Beyond Basins of Attraction: Quantifying Robustness of Natural Dynamics

Abstract

Properly designing a system to exhibit favorable natural dynamics can greatly simplify designing or learning the control policy. However, it is still unclear what constitutes favorable natural dynamics and how to quantify its effect. Most studies of simple walking and running models have focused on the basins of attraction of passive limit-cycles and the notion of self-stability. We instead emphasize the importance of stepping beyond basins of attraction. We show an approach based on viability theory to quantify robust sets in state-action space. These sets are valid for the family of all robust control policies, which allows us to quantify the robustness inherent to the natural dynamics before designing the control policy or specifying a control objective. We illustrate our formulation using spring-mass models, simple low dimensional models of running systems. We then show an example application by optimizing robustness of a simulated planar monoped, using a gradient-free optimization scheme. Both case studies result in a nonlinear effective stiffness providing more robustness.

arXiv comment15 pages. This work has been accepted to IEEE Transactions on Robotics (2019)

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• Momentum Control with Hierarchical Inverse Dynamics on a Torque-Controlled Humanoid
• Real-Time Control for Autonomous Racing Based on Viability Theory
• Stability Principle Underlying Passive Dynamic Walking of Rimless Wheel
• Sample Efficient Optimization for Learning Controllers for Bipedal Locomotion
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Cited by in corpus (2)

• Safe Value Functions
• Viability of Future Actions: Robust Safety in Reinforcement Learning via Entropy Regularization