Single Rigid Body Dynamics Model

单刚体动力学模型SRBDAdvanced

A simplified dynamics model that treats a whole legged robot as one rigid body and ignores the mass of its legs.

The single rigid body dynamics model is one of the most widely used simplifications in legged-robot control: it assumes the legs are light and treats the whole robot as a single rigid body with mass and rotational inertia, subject only to gravity and the ground-reaction forces at its feet. The state is typically the torso's position, orientation, linear velocity, and angular velocity (12 dimensions total), and the control inputs are the contact force at each foot. A full model has dozens of joints and highly nonlinear equations; SRBD compresses this down to a handful of equations, making it practical for real-time optimization. The landmark example is MIT's convex MPC, developed by Di Carlo and colleagues in 2018 on Cheetah 3: assuming small orientation angles as well, the ground-reaction-force planning problem becomes a convex optimization that can be solved in under 1 millisecond, replanned repeatedly at 20–30 Hz over a horizon of up to 0.5 seconds; the resulting forces are then handed to whole-body or joint-level control to execute. It accounts for more than the inverted pendulum model — orientation and rotation — but still doesn't track how the legs themselves move.

ExampleMIT Cheetah 3 used single-rigid-body convex MPC to achieve standing, trotting, flying trot, pronking, bounding, pacing, a three-legged gait, and a 3D gallop, reaching forward speeds up to 3 m/s, all with the same set of gains and weights (Di Carlo et al., IROS 2018).

Also called: SRBD, Single Rigid Body Model, SRBM
Related: Convex MPC · Model Predictive Control · Centroidal Dynamics · Ground Reaction Force (GRF) · Whole-Body Control · Linear Inverted Pendulum Model (LIPM)
Sources: Di Carlo et al., Dynamic Locomotion in the MIT Cheetah 3 Through Convex Model-Predictive Control (IROS 2018)
Lin et al., Learning Near-global-optimal Strategies for Hybrid Non-convex MPC of Single Rigid Body Locomotion (arXiv:2207.07846)
Kim et al., Highly Dynamic Quadruped Locomotion via Whole-Body Impulse Control and Model Predictive Control (arXiv:1909.06586)