Efficient recursive dynamics algorithms for operational-space control with application to legged locomotion

Abstract

This paper presents new recursive dynamics algorithms that enable operational-space control of floating-base systems to be performed at faster rates. This type of control approach requires the computation of operational-space quantities and suffers from high computational order when these quantities are directly computed through the use of the mass matrix and Jacobian from the joint-space formulation. While many efforts have focused on efficient computation of the operational-space inertia matrix $${\varvec{{\Lambda }}}$$?, this paper provides a recursive algorithm to compute all quantities required for floating-base control of a tree-structure mechanism. This includes the first recursive algorithm to compute the dynamically consistent pseudoinverse of the Jacobian $${\,\, \bar{{\varvec{\!\!J}}}}$$J¯ for a tree-structure system. This algorithm is extended to handle arbitrary contact constraints with the ground, which are often found in legged systems, and uses effective ground contact dynamics approximations to retain computational efficiency. The usefulness of the algorithm is demonstrated through application to control of a high-speed quadruped trot in simulation. Our contact-consistent algorithm demonstrates pitch and roll stabilization for a large dog-sized quadruped running at 3.6 m/s without any contact force sensing, and is shown to outperform a simpler Raibert-style posture controller. In addition, the operational-space control approach allows the dynamic effects of the swing legs to be effectively accounted for at this high speed.