Factor Graph-Based Trajectory Optimization for a Pneumatically-Actuated Jumping Robot

Roboticists have increasingly sought to incorporate mechanical compliance into legged robots to realize a range of potential benefits, from improved agility to resilience in complex environments. A promising approach for building compliance into robot legs is to utilize the pneumatic artificial muscle, a pneumatic actuator with inherent compliance due to the compressibility of air. While previous work has explored the capabilities of pneumatic-muscle driven robots in highly dynamic tasks like jumping, there is a lack of trajectory planning strategies for such robots. In this paper, we detail our approach to planning vertical jumping trajectories for a planar two-legged robot driven by four pneumatic artificial muscles using on/off "burst inflation" control. The trajectory optimization problem is represented as a factor graph and solved with the GTSAM optimizer. A hybrid dynamics approach is used to handle foot-ground contacts. The average jump height error between simulation and experiment across multiple jumping trajectories of varying heights was 9.5 cm; the average RMS error between all four joints was 5.6 deg. This work provides a basis to plan more complex jumping and leaping trajectories for pneumatic muscle-driven robots.