Model-Predictive Control for Legged Robots
Overview
Reliable legged robots could be advantageous to many sectors of society across agriculture, health-care, defense, and disaster response. The mobility afforded by legs offers promise for future robots that can go where people go, either in their place, or by their side. In comparison to their biological counterparts, legged robots are yet to be as mobile and dexterous. Control of legged locomotion is often challenging because of the hybrid nature of the dynamics, the curse of dimensionality due to high-dimensional state spaces, and the fact that dynamic gaits are never instantaneously balanced in a traditional sense.
In our work with quadruped robots, we aim to discover fundamental strategies that would endow the robot with added agility, flexibility, and robustness to navigate challenging terrains and environments. The control strategy at the core of our work is Model Hierarchy Predictive Control (MHPC), which is an extension of traditional Model Predictive Control (MPC) approaches. MHPC is inspired by the neuro-control system of humans and animals, i.e., how humans and animals reason about motion planning in face of challenging environments. Recently, we created and used Cascaded-Fidelity Model Predictive Control (Cafe-MPC), which generalizes on the ideas from MHPC, to control a quadruped executing dynamic movements.
To endow quadruped robots with the ability to do more, especially in work environments designed for humans, it is mandatory that walking robots have manipulators as well. For this reason, our current work on quadruped robots is focusing on using our previously constructed control strategies to control a quadruped robot with an arm during loco-manipulation tasks.
Technical Approach
The control approach adopted in the MHPC work is inspired by the sensorimotor control in humans, which is characterized by a fading level of detail as we reason through the consequences of our actions further out in time. More detailed dynamics are managed over the short-term (e.g., for full-body response to unexpected disturbances), whereas long-term planning requires less detail (e.g., where footstep locations should be). MHPC adopts similar strategy, where short-term planning is based on the whole-body dynamics and long-term planning is based on a simplified template, e.g., Linear Inverted Pendulum (LIP) model. In contrast to past approaches, we aim to unify these planning problems in a single optimization framework. While the template-based planning reduces the computational burden, the whole-body-dynamics based planning endows the robot with more robustness to unexpected disturbances. This approach has potential superiority over traditional template-based planning. We are also studying adaptations of Differential Dynamic Programming (DDP) to solve the underlying optimization problem, which mitigates the curse of dimensionality problem imposed by whole body dynamics. Moreover, we are investigating several improvements of the traditional DDP methodology, to improve upon the quadratic convergence of DDP and to allow the method to handle state and control constraints. Since MHPC is essentially a receding-horizon control, the current solution works to warm start for the optimization in next time window, and, thus, enables rapid convergence using DDP.
Cafe-MPC works in a similar vein to MHPC in that it conducts short-term planning based on the whole-body dynamics of the quadruped robot and long-term planning based on the Single Rigid Body (SRB) model. Over the course of the planning horizon, the planner also uses increasingly coarse time steps and relaxed constraints to enhance computational efficiency. The Cafe-MPC planner is used in conjunction with a new value-function-based whole body control (VWBC), and is solved with an efficient multiple shooting iLQR solver tailored to hybrid systems. This work has unified whole-body MPC and whole-body quadratic programming (QP), which have been separated in the past.
Recent Work
Publications
Li, He, and Patrick M. Wensing. "Cafe-mpc: A cascaded-fidelity model predictive control framework with tuning-free whole-body control." arXiv preprint arXiv:2403.03995 (2024).
Nganga, John N., He Li, and Patrick M. Wensing. "Second-order differential dynamic programming for whole-body mpc of legged robots." IFAC-PapersOnLine 56.3 (2023): 499-504.
Nganga, John N., and Patrick M. Wensing. "Accelerating hybrid systems differential dynamic programming." ASME Letters in Dynamic Systems and Control 3.1 (2023): 011002.
Kurtz, Vince, et al. "Mini cheetah, the falling cat: A case study in machine learning and trajectory optimization for robot acrobatics." 2022 International Conference on Robotics and Automation (ICRA). IEEE, 2022.
Li, He, Robert J. Frei, and Patrick M. Wensing. "Model hierarchy predictive control of robotic systems." IEEE Robotics and Automation Letters 6.2 (2021): 3373-3380.
Li, He, and Patrick M. Wensing. "Hybrid systems differential dynamic programming for whole-body motion planning of legged robots." IEEE Robotics and Automation Letters 5.4 (2020): 5448-5455.