The popular approach of assuming a control policy and then finding the largest region of attraction (ROA) (e.g., sum-of-squares optimization) may lead to conservative estimates of the ROA, especially for highly nonlinear systems. We present a sampling-based approach that starts by assuming a ROA and then fi nds the necessary control policy by performing trajectory optimization on sampled initial conditions. Our method works with black-box models, produces a relatively large ROA, and ensures exponential convergence of the initial conditions to the periodic motion. We demonstrate the approach on a model of hopping and include extensive verification and robustness checks.
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Feedback motion planning of legged robots by composing orbital Lyapunov functions using rapidly-exploring random trees
We present a sampling-based framework for feed- back motion planning of legged robots. Our framework is based on switching between limit cycles at a fixed instance of motion, the Poincare ́section(e.g.,apex or touchdown),by finding overlaps between the regions of attraction (ROA) of two limit cycles. First, we assume a candidate orbital Lyapunov function (OLF) and define a ROA at the Poincare ́ section. Next, we solve multiple trajectory optimization problems, one for each sampled initial condition on the ROA to minimize an energy metric and subject to the exponential convergence of the OLF between two steps. The result is a table of control actions and the corresponding initial conditions at the Poincare ́ section. Then we develop a control policy for each control action as a function of the initial condition using deep learning neural networks. The control policy is validated by testing on initial conditions sampled on ROA of randomly chosen limit cycles. Finally, the rapidly-exploring random tree algorithm is adopted to plan transitions between the limit cycles using the ROAs. The approach is demonstrated on a hopper model to achieve velocity and height transitions between steps.
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- Award ID(s):
- 1816925
- NSF-PAR ID:
- 10104234
- Date Published:
- Journal Name:
- IEEE Conference on Robotics and Automation
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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