Highly Dynamic Quadruped Locomotion via Whole-Body Impulse Control and Model Predictive Control
TL;DR A convex MPC plans ground reaction forces on a simple lumped-mass model, and a 500 Hz whole-body impulse controller tracks those forces, rather than a body trajectory, using full-body dynamics. On the Mini-Cheetah it runs five gaits outdoors with one set of gains and reaches 3.7 m/s on a treadmill, up from 2.45 m/s with MPC alone.
What they do
Whole-body controllers usually track a commanded body trajectory, which fails for gaits like galloping or bounding where the center of mass cannot be controlled during flight. This paper pairs a low-rate convex MPC, which plans reaction forces over a gait cycle with a simple model, with a high-rate whole-body impulse controller (WBIC). WBIC treats the MPC’s forces as its main command and lets the body drift from its trajectory.
How it works
- MPC. A lumped-mass model, linearized by assuming small roll and pitch and states near the command, gives a QP over reaction forces with friction-cone constraints. A phase-based gait scheduler fixes the contact sequence, which keeps the problem convex. Dropping force variables for swing feet speeds it up over 10x. Footsteps follow a Raibert heuristic.
- WBIC. Prioritized tasks (body orientation, body position, foot position), resolved by null-space projection, give joint position, velocity and acceleration commands. A small QP then finds reaction forces close to the MPC’s, with a relaxation variable on floating-base acceleration so the base can go uncontrolled in flight. Joint torques follow from the full-body dynamics.
- Execution. Joint position and velocity commands feed 40 kHz joint PD loops alongside the torque. A custom dynamics engine with rotor dynamics lets MPC run at 30-40 Hz and WBIC at 500 Hz onboard.
Results
- Treadmill top speed of 3.7 m/s (Froude number 4.65), against 2.45 m/s for their earlier MPC-only controller. The robot touched 4 m/s but fell right after. Hip joints reached 34 rad/s (limit 40 rad/s) and peak power 280 W, above the 250 W actuator spec.
- Outdoors, the same gains and weights ran gallop, pronk, bound, pace and trot at over 1 m/s each, on wet grass and gravel, with only gait type, speed and direction as inputs.
Limitations
The MPC relies on small roll and pitch angles and a predefined contact sequence. Relaxing the floating base ignores its effect on the other tasks. Reported torques are commanded, not measured, and the outdoor results are qualitative. Only Mini-Cheetah is tested; Cheetah 3 and bipeds are left to future work.
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Abstract
Dynamic legged locomotion is a challenging topic because of the lack of established control schemes which can handle aerial phases, short stance times, and high-speed leg swings. In this paper, we propose a controller combining whole-body control (WBC) and model predictive control (MPC). In our framework, MPC finds an optimal reaction force profile over a longer time horizon with a simple model, and WBC computes joint torque, position, and velocity commands based on the reaction forces computed from MPC. Unlike existing WBCs, which attempt to track commanded body trajectories, our controller is focused more on the reaction force command, which allows it to accomplish high speed dynamic locomotion with aerial phases. The newly devised WBC is integrated with MPC and tested on the Mini-Cheetah quadruped robot. To demonstrate the robustness and versatility, the controller is tested on six different gaits in a number of different environments, including outdoors and on a treadmill, reaching a top speed of 3.7 m/s.
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