Cpg based locomotion
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CPG-based LOCOMOTION. Robotics Course. Lesson 23. Legged Robot Locomotion Control. Legged Robot Locomotion Control 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.

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CPG-based LOCOMOTION

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Cpg based locomotion

CPG-based LOCOMOTION

  • Robotics Course

Lesson 23


Legged robot locomotion control

Legged Robot Locomotion Control

  • Legged Robot Locomotion Control

  • CPG-and-reflex based Control of Locomotion


Locust behavior

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

Generation and Regulation of Motion


Neuronal model

Neuronal Model


Spinal rhythm generation

Spinal Rhythm Generation


Half loop model

Half-Loop Model


Cpg fundamentals

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

Recursive Neural Network


Connectivity

Connectivity


Neuromechanical simulation

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

Questions

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

    Automatic setting of network parameters

  • How is traveling wave affected by the intersegmental coupling?

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

  • How is the CPG activity affected by rapidly varying locomotion control


Genetic algorithm

Genetic Algorithm


Fitness functions evolved parameters

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

Example of different stages in an evolutionary run

Generations


Example of evolved swimming controller

Example of evolved swimming controller:


The problems of legged locomotion control

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 control1

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

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 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

Minimal ingredients for locomotion control

  • 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

  • A PID-controller

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


Minimalist control diagram

Minimalist control diagram


Cpg and reflex based control of locomotion

CPG-and-reflex based Control of Locomotion

  • Legged Robot Locomotion Control

  • CPG-and-reflex based Control of Locomotion


Cpg and reflex control

CPG-and-reflex control

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


Concept of limit cycle

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 control1

CPG-and-reflex control

  • Two types of implementations:

    • CPG produces desired positions

  • CPG directly produces torques


Taga s neuromechanical simulation

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 simulation1

Taga's neuromechanical simulation

  • Neural oscillator:(Taga 1994)


Taga s neuromechanical simulation2

Taga's neuromechanical simulation

  • Walking gait:


Taga s neuromechanical simulation3

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 oscillators

Nonlinear oscillators

  • Example:

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

LampreySalamander


Nonlinear oscillator model

Nonlinear oscillator model

  • Each oscillatory center is modeled with the following oscillator

  • Limit cycle: explicit frequency and amplitude parameters

    Limit Cycle


Inter oscillator coupling

Inter-oscillator coupling

  • Two parameters aij and bij per coupling


Body cpg

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

Generation of traveling waves for swimming

Example:

  • Devolvé et. al. (1997)

  • EMG

  • In axial

  • musculature


Corresponding swimming gait

Corresponding swimming gait

Motoneuron signals:mi =  max(xi, 0)


Complete cpg

Complete CPG

  • Limb CPG

Body CPG


Generation of standing wave for walking

Generation of standing wave for walking

  • swimming

EMG


From swimming to walking

From swimming to walking


The salamander model

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.


Cpg based locomotion

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...


Cpg based locomotion

Biological motor behaviour

Central Pattern Generating Neural Networks (CPGs):

Small, relatively simple

neural systems with

well-defined units,

well-defined circuitry, and well-defined function

Brain control

Central Pattern

Generators

Muscles

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


Cpg motor schema

CPG Motor Schema

In “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: walking


Real salamander from walking to swimming

Real salamander: from walking to swimming


Real salamander swimming

Real salamander: swimming


Real salamander from swimming to walking

Real salamander: from swimming to walking


Outcomes

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

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

Kimura Lab.

National Univ. of Electro-Communications

Tokyo


Cpg and reflex control summary

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


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