Biorobotics Laboratory BioRob

Adaptive CPG

Adaptive Four Legged Locomotion Control
Based on Nonlinear Dynamical Systems


Dynamical systems have been increasingly studied in the last decade for designing locomotion controllers. They offer several advantages over previous solutions like synchronization, smooth transitions under parameter variation, and robustness.

We present a locomotion controller for four legged robots.
The controller is composed of a set of coupled nonlinear dynamical systems. Using our controller the robot is capable of adapting its locomotion to the physical properties of the robot, i.e. the resonant frequency.
Our approach aims at developing an on-line learning system that attempts to minimize the energy necessary for the gait. We have implemented the model both on a physical based simulator (Webots) and on a Sony Aibo robot. Our model is supported by a series of experiments which demonstrate how the controller can tune its frequency to the resonant frequency of the robot, and modify it when the weight of the robot is changed.


The controller we propose is suitable for robotic implementation and might be suitable for biological modeling. It adapts its walking frequency to the physical properties of the robot. Hopf oscillators and adaptive frequency oscillators are used as building blocks in the controller. Adaptation is embedded in the dynamical systems, and no external optimization is required. Moreover, adaptation is not a batch process, and the controller adapts its parameters online using proprioceptive signals.

The robot locomotion is based on two different kinds of joints: knees - passively controlled by springs, and hips - actively controlled by servos. The robot swings on the knees behaving like an inverted pendulum.

A Hopf oscillator controls each hip. Each of these oscillators is coupled to the other hips for inter-limbs gait coordination. Moreover, each hip is coupled in phase to the relative knee. This movement coordination permits to recycle the potential energy of the knee springs to push the robot forward.

An Adaptive Frequency Oscillator (AFO) tunes its frequency to the knee oscillations, and this frequency is used for the hip oscillators. This controller has two feedback loops: one permits phase synchronization to proprioceptor signals and the second frequency adaptation.

Simulation Movies (Webots):

In this video the robot start with a walking frequency of 1.27 [Hz] (or 8 [rad/s]): WebotsFrom8.avi

In this video the robot start walking from scratch, it means frequency of 0 [Hz]: WebotsFromScratch.avi

Aibo Real Robot Movies:

In this video the robot swing, and it shows how work the simulated knee spring: AiboSwing.avi

In this video the robot walk from scratch, also with an additional weight of 0.4 [Kg]: AiboWalkFromScratch.avi


How we have simulate a spring on an Aibo knee: aibo_spring.pdf