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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