Robot control
Spring-loaded inverted pendulum model
Definition
The spring-loaded inverted pendulum model represents a running or hopping body as a point mass supported by a massless compliant leg. It captures energy storage and return during stance while omitting most joint and body details.
Also known as: SLIP model, Spring-loaded inverted pendulum
Updated
Reduce a legged body to a spring and mass
The SLIP model places the body's mass at one point and connects it to the ground through a compliant, usually massless leg. During stance, the leg compresses and returns energy. During flight, the point mass follows ballistic motion. Touchdown and liftoff make the model a hybrid system with distinct phases.
Poulakakis and Grizzle use an asymmetric spring-loaded inverted pendulum as the reduced dynamics induced by feedback on a one-legged hopper. Their result shows how a more detailed mechanism can be controlled so that its evolution follows SLIP-like dynamics.
A template for running and hopping
Roboticists use SLIP models to reason about stride energy, touchdown angle, apex state, and periodic running gaits. A controller may plan in the low-dimensional model and then use a whole-body layer to realize the desired leg force or body motion.
The SLIP model differs from the linear inverted pendulum model. LIPM assumes a fixed centre-of-mass height and is commonly used for walking. SLIP includes leg compliance and alternating stance and flight, which makes it better suited to spring-like running or hopping templates.
Template behaviour is not full-robot behaviour
A point mass has no torso orientation, swing-leg inertia, joint limits, foot geometry, or actuator dynamics. A gait that is stable in the reduced model may fail when mapped to a multi-link floating-base robot. Energy loss, damping, terrain compliance, and finite foot contact also change the motion.
The model is most useful when its assumptions are stated and its planned trajectory is checked on the full mechanism. The Poulakakis and Grizzle result concerns a specific hopper and feedback construction; it does not show that arbitrary humanoids naturally reduce to SLIP dynamics.
Sources
Related terms
Bipedal locomotion
Bipedal locomotion is movement using two legs, with body motion coordinated through changing contacts between the feet and the environment. It includes walking and running.
Linear inverted pendulum model
The linear inverted pendulum model approximates a walking robot by a mass moving at constant height above its support, with simplified angular-momentum dynamics. These assumptions make horizontal center-of-mass acceleration linear in the displacement from the support point.
Hybrid zero dynamics
Hybrid zero dynamics is the reduced closed-loop dynamics that remains when a legged robot's controlled outputs are held at zero and that zero set is preserved through impacts. It provides a way to design and analyse periodic gaits in systems with continuous motion and discrete contact events.
Central pattern generator
A central pattern generator is a neural circuit or mathematical oscillator network that produces coordinated rhythmic commands from compact control inputs. In robotics, CPG models are used to generate and modulate repeated motions such as walking, swimming, or wing beating.