Reliable Trajectories for Dynamic Quadrupeds using Analytical Costs and Learned Initializations

Dynamic traversal of uneven terrain is a major objective in the field of legged robotics. The most recent model predictive control approaches for these systems can generate robust dynamic motion of short duration; however, planning over a longer time horizon may be necessary when navigating complex terrain. A recently-developed framework, Trajectory Optimization for Walking Robots (TOWR), computes such plans but does not guarantee their reliability on real platforms, under uncertainty and perturbations. We extend TOWR with analytical costs to generate trajectories that a state-of-the-art whole-body tracking controller can successfully execute. To reduce online computation time, we implement a learning-based scheme for initialization of the nonlinear program based on offline experience. The execution of trajectories as long as 16 footsteps and 5.5 s over different terrains by a real quadruped demonstrates the effectiveness of the approach on hardware. This work builds toward an online system which can efficiently and robustly replan dynamic trajectories.