Locomotion generation for quadruped robots on challenging terrains via quadratic programming

This paper proposes a locomotion generation method for quadruped robots, which first computes an optimal trajectory of the robot’s center of mass (CoM) and then its whole-body motion through inverse kinematics. As the core component, the computing of the CoM trajectory, which is parameterized as polynomials, is based on the robot’s centroidal dynamics and it is observed that several terms in the centroidal dynamics are minor and can be omitted in the locomotion generation. Then, as a basic form of the proposed method, the CoM trajectory optimization is written as a quadratic programming (QP) problem for the case of given step sequences, timings and footholds. Furthermore, the uncertainty of the robot’s CoM, which is described as a convex polyhedron around a nominal CoM position, and the reachability of the robot’s feet, which is approximated as another convex polyhedron, can be added to the QP problem as linear inequality constraints. Ultimately, the planning of step sequences, timings, and footholds is all incorporated, leading to a single mixed-integer quadratic programming problem. Numerical and hardware experiments have been conducted and show that the proposed method can generate various walking motions for a quadruped robot to travel over challenging terrains.