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Bio-inspired locomotion control of hexapods

Bio-inspired locomotion control of hexapods. Alessandro Rizzo. Outline. Bio-inspired robotics CNN-based Central Pattern Generators (CPG) CPG and sensory feedback The VLSI CNN-based CPG chip High-level control HexaDyn and future works. BIO-INSPIRED ROBOTS.

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Bio-inspired locomotion control of hexapods

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  1. Bio-inspired locomotion control of hexapods Alessandro Rizzo

  2. Outline • Bio-inspired robotics • CNN-based Central Pattern Generators (CPG) • CPG and sensory feedback • The VLSI CNN-based CPG chip • High-level control • HexaDyn and future works

  3. BIO-INSPIRED ROBOTS Synergies from various disciplines (robotics, neuroscience, biology, ethology) • Robotic animal models to a major understanding of biological behaviors • Biological inspiration to build efficient robots

  4. REFLEXES IN THE STICK INSECT • Stepping reflex (A) • Elevator reflex (B) • Searching reflex (C) Local reflexes improve rough terrain locomotion in a hexapod robot

  5. Cosa hanno in comune questi animali e il robot?

  6. CPG: a paradigm for bio-inspired locomotion control • Animals move according to a pattern of locomotion • This pattern is due to the pattern of neural activities of the so-called CPG • This paradigm can be used to control a legged robot

  7. Basic definitions for gait analysis • Transfer phase (swing phase, return stroke) • Support phase (stance phase, power stroke) • Cycle time T • Duty factor bi • Leg phase fi • Leg stride l • Leg stroke R • Stroke pitch • Effective body length • Gait matrix • Gait formula • Dimensionless foot position • Dimensionless initial foot position • Kinematic gait formula • Event • Singular gait • Regular gait • Symmetric gait • Support pattern • Periodic gait • Stability margin • Front stability margin (rear stability margin) • Gait stability margin • Stability margin normalized to stride Gait Gait Anatomy/ Structure Stability skip

  8. Tstance (L1) TRIPOD GAIT T Locomotion Patterns – Alternating tripod Duty Factor (df) Leg phases The swing (flexion phase) depends on the mechanics of the limb

  9. Duty Factor (df) Locomotion Patterns – Medium Gait Tstance (L1) MEDIUM GAIT T Leg phases

  10. Locomotion Patterns – Tetrapod Gait Tstance (L1) TETRAPOD GAIT T Duty Factor (df) Leg phases

  11. CPG: a paradigm for bio-inspired locomotion control • Animals move according to a pattern of locomotion • This pattern is due to the pattern of neural activities of the so-called CPG • This paradigm can be used to control a legged robot

  12. Higher Control CPG Central Feedback Sensory feedback Effector Organs Reflex Feedback Environment The Central Pattern Generator • Definition: A neural circuit that can produce a rhythmic motor pattern with no need for sensory feedback or descending control • Proof of existence: remove sensory feedback, descending control and elicit motor pattern • CPG have been demonstrated in all animals to date for rhythmic movements that are essential for survival • Feedforward control The motor system

  13. Neurons and motor-neurons • Action potential (spike) • Beating, Bursting, Silent state • Frequency coding • Synapses: chemical, gap junctions

  14. … Motor-neuron Muscle fiber … Neural Control of Muscles • vertebrates … Muscle fiber Motor-neuron … • arthropods

  15. Flexor Extensor Pair Block • antagonistic pair: flexor – extensor • flexor – extensor modeled by a CNN-based motor unit called CNN neuron more…

  16. 1,1 1,2 1,1 1,2 2,1 2,2 2,1 2,2 3,1 3,1 3,2 3,2 A CPG-based control system • The CPG is realized by a network of coupled nonlinear oscillators through CNNs • Q: How to design a CNN network generating a given pattern? • A: Exploit the analogy with the biological case (synapses, motor-neurons…) • A: Reduce the complexity of the problem

  17. 1,1 1,2 2,1 2,2 3,1 3,2 A CPG-based control system • Ring of N neurons: each neuron is connected to its neighbor with an excitatory (or inhibitory) synapse in a well defined direction (clockwise or counterclockwise) • The behavior of this kind of network for a suitable valuable of the synaptic weight is a well-defined pattern (traveling wave) • The oscillators are synchronized • The phase lags between adjacent oscillators are constant

  18. L1 R3 R2 L2 R1 L3 Fast Gait L1 R3 R2 L2 L3 R1 Slow gait UNIVERSITY OF CATANIA, DEES, SYSTEM AND CONTROL GROUP P. Arena, L. Fortuna, M. Frasca Examples of locomotion patterns with Multi-Template Approach CNN CNN Waveforms (SC circuit) Locomotion pattern

  19. Design of CNN-based CPGFrom Reaction-Diffusion Equations to inhibitory/excitatory connections Skip this section

  20. Higher Control Central Feedback CPG Sensory feedback Effector Organs Reflex Feedback Environment The Central Pattern Generator • The biological paradigm • Pattern of neural activities • Pattern of rhythmic movements • Application in the bio-inspired robotics: the CPG controls the locomotion of an hexapod robot Motor System CNN realization

  21. RD-CNN as CPG for an hexapod robot • Reaction-diffusion equation • CNN implementation of the nonlinear medium • Autowaves (slow-fast dynamics) • Reorganization of the slow part when the pattern is switched into another one • Turing patterns in the higher control level The design of CPG in which also chemical synapses are involved is considered in the following

  22. The Neuron Model - Slow-Fast CNN Neuron • Equations & Parameters • Behavior y1(t), y2(t) ok

  23. Existence of a periodic orbit • Poincaré-Bendixson theorem: • This theorem is a powerful tool to establish the existence of • periodic orbits in 2D flows. • It states that if R is a closed region that does not contain fixed points for the vector field x=f(x) and a trajectory C confined in R does exist, then R contains a closed orbit (and either C is itself the closed orbit or spirals toward to it).

  24. 1,1 a=y2 b=y1 X A D AEP H PEP C B stance a swing b a1 a2 2 DOF leg Leg Controller • Control of a 2 DOF leg: 1 CNN neuron CNN neuron

  25. 1,1 1,2 2,1 2,2 3,1 3,2 y(x) 1 x -1 1 -1 Cellular Neural Networks - Two-layer CNN equations • MxNTwo-layer CNN cell equations • Neighbourhood • PWL Output • Scheme of a CNN layer

  26. The Synapse Model - Chemical Synapse for the Slow-Fast Neuron • Chemical Synapse with excitatory synapse inhibitory synapse • SimplifiedChemical Synapse (excitatory and inhibitory) Template • SimplifiedDelayedChemical Synapse (excitatory and inhibitory) Template y1(t),y2(t) Tc

  27. CNN Multi-Template Approach - Guidelines • Definitions: • N = number of pattern steps • n = number of legs • ring of N neurons = each neuron is connected to its neighbor with an excitatory (or inhibitory) synapse in a well defined direction (clockwise or counterclockwise) • Guidelines • Create a ring of N neurons • Add the n-N neurons by using synchronisation via “coupling” or synchronisation via “duplicating” • Choose the synaptic weights

  28. Rings of N Slow-Fast Neurons • Inhibitory synapses: (a) connections on the layer: A11… (b) connections between layers: A21... (delayed synapses) • The behavior can depend on initial conditions • In the case (b) [“delayed synapse”] patterns with traveling waves in a well defined direction are obtained (a) (b)

  29. B’ B C’ C A B B B’ C A C A ... ... ... ... Adding the n-N neurons • Synchronisation via “coupling” • Synchronisation via “duplicating” Neuron B and neuron B’ are synchronised because they belong to rings that have the same number of cells and share a neuron Neuron B’ and neuron B have the same synaptic inputs

  30. 1,1 1,2 2,1 2,2 3,1 3,2 L1 R3 R2 MTA-CNN: An Example - The Caterpillar Gait Hexapod L1 R3 R2 L2 L3 R1 Two layer 3x2 CNN Scheme of the locomotion pattern: Caterpillar for six legged robots (right and left legs move in synchrony) N=3 • Guidelines (1) • Create a ring of N neurons

  31. L1 L1 R3 R3 L1 R3 e L1 R3 L1 R3 e/2 e R2 R2 L2 L2 R2 L2 e/2 R2 R2 L2 e/2 e/2 e L3 L3 R1 R1 L3 R1 e L3 R1 MTA-CNN: An Example - The Caterpillar Gait • Guidelines (2) • Add the n-N=3 neurons by using synchronisation via “coupling” or synchronisation via “duplicating” Synchronisation by duplicating synapses 1 and 2. Thus, neuron R2 is synchronised with L2 1 1 1 2 2 2 • Guidelines (3) • Choose the synaptic weights

  32. MTA-CNN: An Example - The Caterpillar Gait • Firing Sequence • CNN Implementation: synaptic connections are established by the feedback templates, these templates depend on the cell position (i.e. they are space-variant) R3 L1 L1 L1 R3 R3 R2 R2 R2 L2 L2 L2 L3 R1 L3 R1 R1 L3

  33. MTA-CNN: An Example - The Caterpillar Gait Simulation Results (SPICE) L2 R2 L1 R1 L3 R3

  34. Changing the locomotion pattern R3 L1 • Other locomotion patterns have been implemented (the fast gait, the medium gait and the slow gait) • To change a locomotion pattern a new set of template should be loaded, while the network structure is not varied R2 L2 (a) L3 R1 L1 R3 (b) R2 L2 L3 R1 L1 R3 R2 L2 (c) L3 R1

  35. Conclusions • A new approach for the design of CNN based CPG to control artificial locomotion has been presented • It includes a model of chemical synapses • A neighborhood of r=1 is always used • Each leg is always driven by the same cell in all the gaits • Several locomotion patterns have been successfully implemented on a hexapod robot

  36. CPG and feedback • Observation: The feedback is fundamental for animal (and legged robot) locomotion • How to implement sensory feedback?

  37. Higher Control CPG Central Feedback Sensory feedback Effector Organs Reflex Feedback Environment CPG & Feedback from Sensors Focus of this work is how to include the sensor feedback in the CNN-based CPG

  38. Braitenberg vehicles Sensors • Direct coupling sensor/motor • The speed of the motor is changed according to the output of the sensor • Excitatory/inhibitory connections • “+” increase the speed • “-” decrease the speed • Behavior of the vehicles + + Wheels

  39. Braitenberg vehicles attracted by light + + - -

  40. Braitenberg vehicles – photophobic behavior - - + +

  41. The principles underlying Braitenberg vehicles are used to implement feedback in CNN-based CPG

  42. - - CNN based CPG: obstacle avoidance • Control of direction: including sensor feedback in the CPG for obstacle avoidance as in Braitenberg photophobic vehicle • To this aim the dynamical behavior of the CNN cells controlling the mid legs is changed by acting on the bias parameter

  43. i2=0.34 i2=0.35 i2=0.36 Dynamics of the CNN cell Nullclines

  44. x2 x1 Critical value of the parameter i2 Jacobian of the system for y1=-1

  45. Period of oscillations T versus bias values • Continuous line • Diamonds: Numerical data

  46. obstacle - - CNN-based CPG with sensor feedback obstacle SLX SRX L1 R1 L2 R2 L3 R3 • The hexapod is equipped with two sensors (measuring the distance from an obstacle) • Feedback from sensors is included in the CNN-based CPG

  47. HEXAPOD (VISUAL NASTRAN) CNN CPG (MATLAB) Control Scheme antennae output • Simulation tools • The CPG is implemented in MATLAB • A dynamical simulator of the hexapod robot is provided by VisualNastran

  48. Results Video

  49. Signals from CPG

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