Convex Model Predictive Control of Single Rigid Body Model on SO(3) for Versatile Dynamic Legged Motions

This paper presents a convex model predictive control framework for versatile dynamic legged motions with negligible leg dynamics. The framework utilizes the single rigid body model linearly approximated around the operating point. With ground reaction forces as direct control inputs to the system, no reference control trajectory needs to be specified in advance. By using the rotation matrix for the evolution of rotational dynamics, issues arising from other representations can be avoided. Moreover, the rotation matrix is parametrized using the history of angular velocity without introducing additional variables. The effect is that we can still take the orientation into consideration efficaciously without directly working on it. The framework tackles the robot reference tracking problem via trajectory optimization, which is formulated into a standard quadratic program and can be solved efficiently in real time with guaranteed optimality. It was verified on various legged robots with different numbers of legs for performing different types of dynamic motions in the simulation environment. We thus envision a promising future of the proposed convex model predictive control framework in legged robots and potentially in other applications as well.