Variational-Based Optimal Control of Underactuated Balancing for Dynamic Quadrupeds

This paper presents a control strategy for quadruped balancing that enables postural control in underactuated contact configurations (e.g., when standing on two point feet). Underactuated balancing has received considerable attention with prototype control models such as the cart pendulum or acrobot. Yet, when attempting to transition these solutions to balance in legged robots, technical challenges related to friction-limited contacts and the underlying manifold structure of the configuration space prevent straightforward application. This paper presents a new balance control framework that combines constrained optimal control strategies with recent variational-based linearization approaches to solve the balancing problem for a common simplified quadruped model. The controller is implemented as a convex quadratic program (QP) that uses an unconstrained optimal control solution to approximate a friction-constrained optimal policy. Unlike state-of-the-art QP-based balance controllers, the method is able to handle balance in underactuated regimes. Via comparison to model-predictive control strategies, the proposed formulation is highly compact, requiring less computation, while still showing the ability to handle extreme friction limitations. Simulation and hardware results with the MIT Mini Cheetah demonstrate the capabilities of the controller to exploit body angular momentum for disturbance recovery on two feet, and to recover from cases where the center of mass exits the support polygon. These results and the generality of the formulation suggest exploration for further application to bipeds and humanoids.