Control Policies for a Large Region of Attraction for Dynamically Balancing Legged Robots: A Sampling-Based Approach

Abstract

SUMMARY 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 an ROA and then finds 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.

Control Synergies for Rapid Stabilization and Enlarged Region of Attraction for a Model of Hopping

“…A better approach, particularly useful for a large number of fixed points, would be to fit a control law (e.g., quadratic function, neural networks, etc.) for each control action to simplify online implementation [52,53,54]. We have ignored actuator limits and kinematic limits, which will restrict the region of attraction to smaller ellipses, particularly at faster speeds.…”

An approach to drastically reduce the required legs DOFs for bipedal robots and lower-limb exoskeletons

“…Bipedal robots are important because they offer autonomous, human-like mobility in an environment built for human activities [1,2]. In an indoor environment, for example, they are a useful tool for moving around objects, interacting with humans, and assisting to collaborate with humans in simple tasks [3,4]. They have a tremendous future promise in terms of assisting humans as a robotic laborer, maid, and elderly care.…”