Convex MPC for Quadruped Locomotion
Convex MPC is a structured set of notes on dynamic quadruped locomotion, from rigid-body dynamics and contact constraints to optimal ground-reaction-force planning and real-time gait control.
The series develops a convex formulation that plans forces over a fixed-timing gait while minimizing a finite-horizon tracking cost. The same theory is evaluated on the ANYmal C robot in MuJoCo, and the C++ implementation can be compiled to WebAssembly for interactive visualization.
How to read this series
- Rigid-body dynamics sets up the equations of motion for a quadruped as a single rigid body with four point contacts.
- Single-rigid-body model simplifies the dynamics to a 13-state model and derives its linearization and discretization.
- MPC formulation converts trajectory tracking into a condensed quadratic program (QP) solved at 40 Hz.
- Gait and swing control explains how fixed-timing gait phases interact with force planning and independent swing-leg trajectories.
- Practical implementation discusses solver timing, numerical conditioning, parameter tuning, and deployment choices.
- Series summary brings the complete quadruped control loop together.