Augmenting Reduced-Order Control for Push Recovery with Full-Order Balance Stability Basins

Abstract Robust push recovery controllers must stabilize a system in response to various perturbations. Existing approaches often determine these actions based on reduced-order models, which can either underutilize the system's capabilities or lead to dynamic infeasibility. This study addresses this gap by integrating balanced state basins, computed from whole-body dynamics, into a partition-aware controller. These basins represent sets in center-of-mass state space, from which a robot with an idealized controller can achieve a desired equilibrium state, subject to contact requirements such as step length. The basins are constructed using an optimization framework that incorporates whole-body dynamics alongside system- and task-specific constraints. Polynomial regression is used to approximate the basin as a function of step length. The parameterized basins partition the state space into regions requiring a step and those that do not, serving as a decision boundary between the non-stepping and stepping strategies. The non-stepping sub-controller is designed to return the system to a static equilibrium without changing contact and uses an iterative linear quadratic regulator with a single-rigid-body-inspired model for efficient trajectory optimization. The stepping sub-controller models the system dynamics as a passive 3D pendulum and uses a capture-point-based planner to achieve a stabilizing step. The combined use of these sub-controllers and basin estimation enables multi-step balance recovery despite planning only one step at a time. Real-time simulations demonstrate the controller's potential to augment the computational efficiency of reduced-order models with the dynamic feasibility guarantees of full-order balanced state basins.