CPG-based LOCOMOTION

Lesson 23Lesson 23

Robotics Course

Legged Robot Locomotion Control

1. Legged Robot Locomotion Control

2. CPG-and-reflex based Control of Locomotion

Locust Behavior

Leg Coordination: A number of local rules suffice for different gaits like tripod or tetrapod to emerge.

Quasi-rhythmic movement of the leg: is controlled by a modular system exploiting the loop through the world. A central oscillator is not necessary.

Control of stance is extremely simplified by application of a combination of negative and positive feedback at the joint level.

This is possible because physics are exploited instead of explicit calculation of a body model.

The system is not only „intelligent“ in terms of its behavioral properties, but also in terms of simplicity of construction.

Generation and Regulation of Motion

Neuronal Model

Spinal Rhythm Generation

Half-Loop Model

CPG Fundamentals

Supraspinal structures are not necessary for producing the basic motor pattern for stepping.

The basic rhythmicity of stepping is produced by neuronal circuits contained entirely within the spinal cord.

The spinal circuits can be activated by tonic descending signals from the brain.

The spinal pattern-generating networks do not require sensory input but nevertheless are strongly regulated by input from limb proprioceptors.

Recursive Neural Network

Connectivity

Neuromechanical simulation

Two-dimensional biomechanical model:

articulated rigid body with spring-and-damper muscles

A model of the body is essential for understanding locomotion control

Questions

1.Is a genetic algorithm a useful tool for designing neural network simulations of the lamprey’s locomotor circuit?

Automatic setting of network parameters

1.How is traveling wave affected by the intersegmental coupling?

2.How is sensory feedback integrated into the CPG for swimming in non-stationary conditions?

3.How is the CPG activity affected by rapidly varying locomotion control

Genetic Algorithm

Fitness functions & evolved parameters

Incremental evolution: first segmental oscillator, then intersegmental couplings, finally sensory feedback

Parameters which are evolved:

Synaptic weights

The fitness functions reward:

Stable oscillations

Variable frequencies (pattern modulation)

Optimized speed of locomotion

The general layout of the neural network is otherwise fixed

Example of different stages in an evolutionary run

Generations

Example of evolved swimming controller:

The Problems of legged locomotion control

Coordinating all the degrees-of-freedom of the robot: finding the right frequency = 1/T, phase , amplitude A and signal shape

The Problems of legged locomotion control

Underactuated problem: a robot cannot follow arbitrary motion commands

Requirements:

Take advante of the robot's dynamics

Coordinate multiple degrees of freedom

Keep balance

Modify the gait for different speed and directions

Obstacle avoidance

Visually-guided feet placements

Adapting to perturbations

Different types of Gaits

Hexapod locomotion: tripod gait, metachronal wave

Quadruped locomotion: walk, trot, gallop/bound, pace

Biped locomotion: walk (at least one leg on the ground at all times), running

Statically versus dynamically stable gaits

Statically stable gait: the center of mass is maintained at all times above the support polygon formed by the contacts between the limbs and the ground

Dynamically stable gait: the center of mass is maintained over the support area only in average

Minimal ingredients for locomotion control

1. A trajectory planner

To produce the different trajectories that each degree of freedom (DOF) has to follow

Trajectory = set of joint angles over the times

2. A PID-controller

To produce the torques (in the motors) necessary to follow a specific trajectory

Minimalist control diagram

CPG-and-reflex based Control of Locomotion

1. Legged Robot Locomotion Control

2. CPG-and-reflex based Control of Locomotion

CPG-and-reflex control

Main idea: use oscillators and replicate the distribute control mechanisms found in vertebrates

Concept of Limit Cycle

A limit cycle is an oscillatory regime in a dynamical system:

If the limit cycle is stable, the states of the system will return to it after perturbations

CPG-and-reflex control

Two types of implementations:

CPG produces desired positions

CPG directly produces torques

Taga's neuromechanical simulation

G. Taga. Emergence of bipedal locomotion through entrainment among the neuro-musculo-skeletal system and the environment. Physica D: Nonlinear Phenomena. 75(1-3):190-208, 1994

G. Taga. A model of the neuro-musculo-skeletal system for human locomotion. I. Emergence of basic gait. Biological Cybernetics, 73(2):97:111, 1995.

Taga's neuromechanical simulation

Neural oscillator:(Taga 1994)

Taga's neuromechanical simulation

Walking gait:

Taga's neuromechanical simulation

Interesting aspects:

Locomotion seen as a limit cycle due to the global entrainment between the neuro-musculo-skeletal system and the environment

Robustness against (small) variations in the environment (e.g. small slopes

Cons

Hand-tuning of (many) parameters to obtain satisfactory limit cycles

Nonlinear oscillatorsExample:

Design a locomotion controller inspired by the salamander CPG for the control of an amphibious robot

Lamprey Salamander

Nonlinear oscillator modelEach oscillatory center is modeled with the following oscillator

Limit cycle: explicit frequency and amplitude parameters

Limit CycleLimit Cyclex = a2−x2− y2

a2 ∗ xτ

− ω0 y

y = ω0 xy = a sin ωt+φ

Inter-oscillator coupling

Two parameters aij and bij per coupling

x = a2−x2− y2

a2 ∗ xτ

− ω0 y ∑j

ai j∗x j +bi j∗y j

y = ω0 x

Body CPG

Model: 40 segments

Assumptions:

Lamprey-like system: chain of oscillators;

Two oscillators per segment

Closest neighbour coupling

Double symmetry:

Left-right per segment

6 open coupling parameters

Generation of traveling waves for swimming

Devolvé et. al. (1997)

EMG

In axial

musculature

Example:

Corresponding swimming gait

Motoneuron signals: mi = max(x

i , 0)

Complete CPG

Limb CPG Body CPG

Generation of standing wave for walkingswimming

EMG

From swimming to walking

The salamander model

The strength:

We need not have knowledge of the biology to define a fitness function that gives rise to efficient and robust locomotion. A fitness function that rewards fast forward motion might suffice.

The weakness:

If we wanted to model a real salamander, we are in for a disappointment. The neural network that evolved bares little resemblance to the biological one.

What does it do?

The salamander can:

• Walk• Swim • Switch between walking & swimming across a border• Switch to swimming if it falls into the water• Follow targets, turn, modulate speed, and more...

Biological motor behaviour

Central Pattern Generating Neural Networks (CPGs):

Small, relatively simple neural systems withwell-defined units, well-defined circuitry, and well-defined function

Such central pattern generators are believed to be responsible for practically all known muscle behaviour.

Brain control

Central PatternGenerators

Muscles

CPG Motor SchemaIn “simple” motor systems (insects, molluscs, crustacea), central pattern generators have identical architectures in all animals of the same species.

They are typically distributed throughout the body and form a distributed coordinated network of activity.

They also receive high level instructions from the brain and feedback from the low-level muscles.

The salamander model, while it is ‘high level’ its fitness function, is based on a simulation of CPGs and muscles.

Real salamander: walking

Real salamander: from walking to swimming

Real salamander: swimming

Real salamander: from swimming to walking

Outcomes

Simple control signals for controlling the speed, direction and type of gait (abody_left, abody_right, alimb_left, alimb_right and )

Robustness against noise and perturbations

Entrainment between the CPG and the body through sensory feedback

Nonlinear oscillators are more tractable then neural networks (fewer parameters)

Problems: not yet a good methodology for setting the coupling weights

Quadruped-robot controlled with a CPG-and-reflex based controller

Kimura Lab.National Univ. of Electro-Communications

Tokyo

CPG-and-reflex Control: summary

Pros:

Distributed control

Limit cycle behavior (controller-body-environment)

Robust against perturbations

Smooth trajectories due to the oscillators

Cons:

Fewer mathematical tools than other methods

Not (yet) a clear design methodology, it is recommended to use learning algorithms