Frequency-Aware Model Predictive Control
This work addresses the problem of robust motion planning for legged robots in unstructured environments, offering a method to handle bandwidth limitations, though it is incremental as it builds on existing trajectory optimization techniques.
The paper tackled the challenge of transferring trajectory optimization solutions to robotic hardware by addressing unmodeled dynamics like compliant contacts and actuator bandwidth limits, proposing frequency-shaped cost functions in model predictive control for legged robots, which resulted in significantly improved tracking performance and robust walking on terrain with unmodeled compliance in experiments with the ANYmal quadruped.
Transferring solutions found by trajectory optimization to robotic hardware remains a challenging task. When the optimization fully exploits the provided model to perform dynamic tasks, the presence of unmodeled dynamics renders the motion infeasible on the real system. Model errors can be a result of model simplifications, but also naturally arise when deploying the robot in unstructured and nondeterministic environments. Predominantly, compliant contacts and actuator dynamics lead to bandwidth limitations. While classical control methods provide tools to synthesize controllers that are robust to a class of model errors, such a notion is missing in modern trajectory optimization, which is solved in the time domain. We propose frequency-shaped cost functions to achieve robust solutions in the context of optimal control for legged robots. Through simulation and hardware experiments we show that motion plans can be made compatible with bandwidth limits set by actuators and contact dynamics. The smoothness of the model predictive solutions can be continuously tuned without compromising the feasibility of the problem. Experiments with the quadrupedal robot ANYmal, which is driven by highly-compliant series elastic actuators, showed significantly improved tracking performance of the planned motion, torque, and force trajectories and enabled the machine to walk robustly on terrain with unmodeled compliance.