Raibert Heuristic

A foot-placement rule that shifts the landing spot forward or back based on body speed to regulate a legged robot's forward motion.

The Raibert heuristic comes from Marc Raibert's work on single-leg hopping robots at Carnegie Mellon University in the early 1980s (his lab later moved to MIT and became the Leg Lab). He split hopping control into three independent parts — hop height, body attitude, and forward speed — with forward speed regulated through foot placement. The landing spot, relative to the hip, is x_f = ẋ·T_s/2 + k·(ẋ − ẋ_d), where ẋ is the current forward speed, T_s is the stance-phase duration, ẋ_d is the desired speed, and k is a feedback gain. The first term is the ‘neutral point’: landing there lets the body pass symmetrically fore and aft over the foot during stance, leaving speed roughly unchanged. The second term is a correction — running faster than desired shifts the foot forward to decelerate, and running slower shifts it back to accelerate. The heuristic needs no full dynamics model, and variants of it are still used today by quadruped controllers such as MIT Cheetah to plan where the swing leg should land, leaving the support-force computation to MPC or whole-body control.

ExampleMIT's open-source Cheetah-Software computes swing-leg placement in its convex-MPC gait controller as 'velocity × stance duration × 0.5 + 0.03 × (actual velocity − desired velocity)', plus a turning correction term — a direct variant of the Raibert formula.

Also called

Raibert Foot Placement, Raibert's Foot Placement Formula

Related

Footstep Planning · Swing Foot Trajectory Planning · Convex MPC · Capture Point · Spring-Loaded Inverted Pendulum · Quadruped Robot

Sources

MIT Leg Laboratory: 3D One-Leg Hopper (1983–1984)
mit-biomimetics/Cheetah-Software: ConvexMPCLocomotion.cpp（footstep placement）
Di Carlo et al., Dynamic Locomotion in the MIT Cheetah 3 Through Convex Model-Predictive Control (2018)