Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds

In this letter, we present a trajectory optimization framework for whole-body motion planning through contacts. We demonstrate how the proposed approach can be applied to automatically discover different gaits and dynamic motions on a quadruped robot. In contrast to most previous methods, we do not prespecify contact-switches, -timings, -points or gait patterns, but they are a direct outcome of the optimization. Furthermore, we optimize over the entire dynamics of the robot, which enables the optimizer to fully leverage the capabilities of the robot. To illustrate the spectrum of achievable motions, we show eight different tasks, which would require very different control structures when solved with state-of-the-art methods. Using our trajectory optimization approach, we are solving each task with a simple, high level cost function and without any changes in the control structure. Furthermore, we fully integrate our approach with the robot's control and estimation framework such that we are able to run the optimization online. Through several hardware experiments, we show that the optimized trajectories and control inputs can be directly applied to physical systems.