Fast Contact-Implicit Model-Predictive Control (2107.05616v3)

Abstract: We present a general approach for controlling robotic systems that make and break contact with their environments. Contact-implicit model predictive control (CI-MPC) generalizes linear MPC to contact-rich settings by utilizing a bi-level planning formulation with lower-level contact dynamics formulated as time-varying linear complementarity problems (LCPs) computed using strategic Taylor approximations about a reference trajectory. These dynamics enable the upper-level planning problem to reason about contact timing and forces, and generate entirely new contact-mode sequences online. To achieve reliable and fast numerical convergence, we devise a structure-exploiting interior-point solver for these LCP contact dynamics and a custom trajectory optimizer for the tracking problem. We demonstrate real-time solution rates for CI-MPC and the ability to generate and track non-periodic behaviours in hardware experiments on a quadrupedal robot. We also show that the controller is robust to model mismatch and can respond to disturbances by discovering and exploiting new contact modes across a variety of robotic systems in simulation, including a pushbot, planar hopper, planar quadruped, and planar biped.

• The paper’s primary contribution is a contact-implicit MPC framework that integrates time-varying LCPs with a structure-exploiting interior-point solver for rapid, dynamic control.
• It demonstrates real-time generation of contact-mode sequences on various robotic platforms, including quadrupedal robots and pushbots, ensuring robust performance.
• The approach effectively handles model discrepancies and disturbances, offering promising advancements for control in unstructured, contact-rich environments.

Fast Contact-Implicit Model Predictive Control

The paper "Fast Contact-Implicit Model Predictive Control" presents an innovative approach to controlling robotic systems that engage in frequent contact interactions with their environments. This work builds upon the conventional Model Predictive Control (MPC) framework, extending it to handle contact-rich scenarios using a Contact-Implicit Model Predictive Control (CI-MPC) methodology.

The CI-MPC algorithm generalizes linear MPC using a bi-level approach where the lower-level planning problem is structured around time-varying Linear Complementarity Problems (LCPs). These LCPs are computed using Taylor representations based on a reference trajectory, allowing the dynamics to consider contact timing and forces. A primary contribution of the paper is the development of a structure-exploiting interior-point solver for these LCP-based contact dynamics, enhancing the reliability and speed of numerical convergence.

The paper demonstrates the CI-MPC framework's capability to solve in real-time, enabling it to generate new contact-mode sequences dynamically on quadrupedal robotic hardware. Moreover, it shows resilience to model discrepancies and disturbances, highlighting its applicability across various robotic systems, such as a pushbot, planar hopper, and quadrupedal robots.

Numerical Results and Claims

Significant numerical results are presented demonstrating the solver's speed and robustness across simulations and hardware implementations. The CI-MPC consistently achieved solution rates that facilitated dynamic control of robots across several complex tasks. Notable is the claim that CI-MPC can dynamically adjust to unplanned disturbances, discovering and utilizing new contact modes online—a feature that sets it apart from more restrictive models that depend heavily on predefined sequences.

Implications and Future Directions

The implications of CI-MPC are profound both in practical and theoretical contexts. From a practical standpoint, this methodology allows for robust real-time control in unstructured environments where traditional models may falter due to lack of flexibility in contact handling. This can lead to advancements in the deployment of legged robots for search and rescue missions, exploration, and daily assistive technologies.

Theoretically, CI-MPC opens new avenues in understanding and applying contact-rich control mechanisms in robotics. The application of interior-point methods, with implicit differentiation to solve LCPs, sets a foundation for further exploration into smoother gradient representations in systems traditionally hindered by non-smooth dynamics.

For future work, the authors suggest improvements in trajectory generation, stability, and adaptability of CI-MPC methods across diverse robotic architectures. There is potential for developing more scalable and generalized control strategies leveraging CI-MPC methodologies, particularly in manipulation and dexterous robotics fields where contact dynamics play a critical role.

In conclusion, this paper provides a substantial leap towards enabling dynamic, real-time control in environments with complex contact interactions. Fast Contact-Implicit Model Predictive Control represents a promising step towards advanced, flexible robotics, capable of navigating and interacting with the intricate landscapes they operate in.