Single rigid body model

Reduce an articulated robot to one body#

A humanoid or quadruped contains many moving links, but a single rigid body model collects the main mass and rotational inertia into one body. The feet or other contacts apply external forces at chosen points. Those forces change the body's linear and angular momentum under gravity.

This reduction resembles centroidal dynamics, but it makes a stronger modelling choice: the represented inertia belongs to one rigid body rather than changing with the full joint configuration. It is therefore much smaller than a full floating-base robot model.

Plan body motion and contact forces quickly#

An optimizer can use an SRBM to choose body position, orientation, contact timing, and ground-reaction forces without solving for every joint at the same time. That makes it useful inside model predictive control or for generating reference trajectories that a lower-level controller tracks.

Batke and colleagues used an SRBM to optimize libraries of bipedal maneuvers, then incorporated the references into reinforcement-learning rewards for Cassie. They added transferability constraints before applying the reduced trajectories to the full robot. Their hardware demonstrations support that particular pipeline, not every SRBM-based plan.

Missing limb dynamics still matter#

Swinging a heavy leg or arm can change whole-body angular momentum and actuator loading. A basic SRBM does not capture those internal motions, joint limits, self-collision, or detailed foot mechanics. A contact force that is feasible for the reduced body may still require an unreachable posture or excessive joint torque.

The model is most useful when its omissions are acceptable for the planning decision and a full-order controller or feasibility check handles the articulated robot. Fast computation does not make the approximation valid for every maneuver.