Dynamic Locomotion in the MIT Cheetah 3 Through Convex Model-Predictive Control

By Jared Di Carlo, Patrick M. Wensing, Benjamin Katz, Gerardo Bledt, Sangbae Kim. IEEE/RJS International Conference on Intelligent RObots and Systems, 2018

797 citations recorded by the source corpus.

This paper presents an implementation of model predictive control (MPC) to determine ground reaction forces for a torque-controlled quadruped robot. The robot dynamics are simplified to formulate the problem as convex optimization while still capturing the full 3D nature of the system. With the simplified model, ground reaction force planning problems are formulated for prediction horizons of up to 0.5 seconds, and are solved to optimality in under 1 ms at a rate of 20–30 Hz. Despite using a simplified model, the robot is capable of robust locomotion at a variety of speeds. Experimental results demonstrate control of gaits including stand, trot, flying-trot, pronk, bound, pace, a 3-legged gait, and a full 3D gallop. The robot achieved forward speeds of up to 3 m/s, lateral speeds up to 1 m/s, and angular speeds up to 180 deg/sec. Our approach is general enough to perform all these behaviors with the same set of gains and weights.

Subfields: Biomedical Engineering, Civil and Structural Engineering

View Paper: https://www.semanticscholar.org/paper/608d53fcd69173d30914e29d9b8ca4b37efe9ac4

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Citations in the corpus

Highly Dynamic Quadruped Locomotion via Whole-Body Impulse Control and Model Predictive Control (2019, methodology): “In our previous work, we demonstrated that convex MPC can perform various dynamic gaits at high speed on both Cheetah 3 [8] and Mini-Cheetah [9].”
On the Sample Complexity of Stability Constrained Imitation Learning (2021, methodology): “We used the same Z − Y − X Euler angle conventions in [35] to represent the CoM rotation.”
Real-world humanoid locomotion with reinforcement learning (2023, background): “While classical control methods can achieve stable and robust locomotion ( 6–9 ), optimization-based strategies have shown the advantage of simultaneously authoring dynamic behaviors and obeying constraints ( 10–12 ).”
RMA: Rapid Motor Adaptation for Legged Robots (2021, positive): “MIT Cheetah 3 [5] can achieve high speed and jump over obstacles by using regularized model predictive control (MPC) and simplified dynamics [12].”
Mini Cheetah: A Platform for Pushing the Limits of Dynamic Quadruped Control (2019, methodology): “For locomotion, we use Convex Model Predictive Control (cMPC) as describe in [13].”
Learning Agile Robotic Locomotion Skills by Imitating Animals (2020, background): “Trajectory optimization and model predictive control can mitigate some of the manual effort involved in the design process, but due to the high-dimensional and complex dynamics of legged systems, reduced-order models are often needed to formulate tractable optimization problems [11, 17, 12, 2].”
MIT Cheetah 3: Design and Control of a Robust, Dynamic Quadruped Robot (2018, background): “In recent work [17] approximate dynamics are enforced with linear equality constraints based on a time-varying approximation that enables formulating the MPC problem as a quadratic program.”
Data Efficient Reinforcement Learning for Legged Robots (2019, methodology): “With handcrafted models, a number of efﬁcient planning algorithms have been tested for robot loco-motion [19, 20, 21].”
Crocoddyl: An Efficient and Versatile Framework for Multi-Contact Optimal Control (2019, background): “Recent work on optimal control has shown that nonlinear Model Predictive Control (MPC) is plausible for controlling legged robots in real-time [15], [16], [17].”
Learning to Walk via Deep Reinforcement Learning (2018, methodology): “For example, the MIT Cheetah [5] uses a state machine over contact conditions, generates simple reference trajectories, performs model predictive control [9] to plan for desired contact forces, and then uses Jacobian transpose control to realize them.”