Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds

In this work 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 pre-specify 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. In total we show 7 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 integrated our approach with the robots control and estimation framework such that optimization can be run online. By demonstrating a rough manipulation tasks with multiple dynamic contact switches, we show that the optimized trajectories and control inputs can be directly executed on hardware.