Feedback MPC for Torque-Controlled Legged Robots (1905.06144v2)

Abstract: The computational power of mobile robots is currently insufficient to achieve torque level whole-body Model Predictive Control (MPC) at the update rates required for complex dynamic systems such as legged robots. This problem is commonly circumvented by using a fast tracking controller to compensate for model errors between updates. In this work, we show that the feedback policy from a Differential Dynamic Programming (DDP) based MPC algorithm is a viable alternative to bridge the gap between the low MPC update rate and the actuation command rate. We propose to augment the DDP approach with a relaxed barrier function to address inequality constraints arising from the friction cone. A frequency-dependent cost function is used to reduce the sensitivity to high-frequency model errors and actuator bandwidth limits. We demonstrate that our approach can find stable locomotion policies for the torque-controlled quadruped, ANYmal, both in simulation and on hardware.

• The paper introduces a DDP-based Feedback MPC that eliminates the need for a separate tracking controller, ensuring smoother locomotion for torque-controlled legged robots.
• It incorporates a relaxed barrier function to manage friction-induced inequality constraints, enhancing stability under varying contact conditions.
• The study employs a frequency-aware cost function to suppress high-frequency errors, with successful validation on ANYmal at update rates as low as 15 Hz.

Feedback MPC for Torque-Controlled Legged Robots: An Overview

The paper tackles a prevalent issue in the domain of legged robotics: the computational limitations of mobile robots, which hinder the application of Model Predictive Control (MPC) at the desired torque level for whole-body control. The research presents a strategic development in utilizing a Differential Dynamic Programming (DDP)-based MPC algorithm to bridge the gap between low MPC update rates and high-frequency actuation command requirements.

Key Contributions

1. Single-Stage Feedback Policy: The authors propose utilizing the feedback policy derived from a DDP-based MPC algorithm, eliminating the need for a separate tracking controller often employed to mitigate model discrepancies due to low update rates. This approach ensures a continuous control signal, thus maintaining smoother locomotion for the quadruped robot, ANYmal.
2. Handling Inequality Constraints: The problem of inequality constraints arising from friction is addressed by incorporating a relaxed barrier function into the MPC framework. This integration allows for improved handling of constraints, which is crucial for maintaining stable robot locomotion under varying contact conditions.
3. Frequency-Aware Cost Function: By employing a frequency-dependent cost function, the authors aim to suppress the influence of high-frequency model errors, thereby enhancing the robustness of the control strategy. This technique aligns the bandwidth of the feedback policy with the physical capabilities of the robot's actuators.
4. Implementation and Validation: The authors offer empirical evidence by testing their feedback MPC approach on the quadruped robot in both simulated and real-world environments. Remarkably, robust locomotion was achieved even with an MPC update frequency as low as 15 Hz, showcasing the approach's adaptability for onboard execution with constrained computational resources.

Results and Implications

The application of MPC with an integrated feedback mechanism developed from the DDP-based algorithm resulted in significant qualitative improvements in the locomotion of ANYmal. The reduction in controller dependency, coupled with sa mple rate adaptability, marks a step forward in managing the computational challenges faced in real-time robotic control scenarios. The manipulation of barrier functions and frequency-aware methods also demonstrates the feasibility of utilizing advanced control strategies to meet physical actuator constraints more naturally.

Future Directions

The research suggests several avenues for future work, primarily focusing on refining system models for broader environmental interactions and enhanced computational methods to further lower the needed update rates, thereby improving efficiency without sacrificing stability or performance. Enhanced robustness through the incorporation of more complex constraints or adaptive learning-based paradigms could be explored to further augment the capabilities of torque-controlled robotic systems.

This paper advances the discourse in legged robot control by providing a sophisticated framework that judiciously balances computational demands with practical control requirements, paving the way for more adaptable and efficient legged robotic systems in dynamic environments.