Abstract-We present a single trajectory optimization formulation for legged locomotion that automatically determines the gait sequence, step timings, footholds, swing-leg motions, and sixdimensional body motion over nonflat terrain, without any additional modules. Our phase-based parameterization of feet motion and forces allows to optimize over the discrete gait sequence using only continuous decision variables. The system is represented using a simplified centroidal dynamics model that is influenced by the feet's location and forces. We explicitly enforce friction cone constraints, depending on the shape of the terrain. The nonlinear programming problem solver generates highly dynamic motion plans with full flight phases for a variety of legged systems with arbitrary morphologies in an efficient manner. We validate the feasibility of the generated plans in simulation and on the real quadruped robot ANYmal. Additionally, the entire solver software TOWR, which used to generate these motions is made freely available. Index Terms-Legged robots, motion and path planning, optimization and optimal control, humanoid and bipedal locomotion.
Winkler et al. REF recently proposed another direct method (without complementarity constraints) based on a continuous parameterization of feet motion and forces to generate gait sequences.
Gait and Trajectory Optimization for Legged Systems Through Phase-Based End-Effector Parameterization
IEEE Robotics and Automation Letters
IEEE Robotics and Automation Letters
Engineering