Lifted contact dynamics for efficient optimal control of rigid body systems with contacts

We propose a novel and efficient lifting approach for the optimal control of rigid-body systems with contacts to improve the convergence properties of Newton-type methods. To relax the high nonlinearity, we consider the state, acceleration, contact forces, and control input torques, as optimization variables and the inverse dynamics and acceleration constraints on the contact frames as equality constraints. We eliminate the update of the acceleration, contact forces, and their dual variables from the linear equation to be solved in each Newton-type iteration in an efficient manner. As a result, the computational cost per Newton-type iteration is almost identical to that of the conventional non-lifted Newton-type iteration that embeds contact dynamics in the state equation. We conducted numerical experiments on the whole-body optimal control of various quadrupedal gaits subject to the friction cone constraints considered in interior-point methods and demonstrated that the proposed method can significantly increase the convergence speed to more than twice that of the conventional non-lifted approach.