t for Two: Linear Synergy Advances the Evolution of Directional Pointing Behaviour Marieke Rohde & Ezequiel Di Paolo Centre for Computational Neuroscience and Robotics University of Sussex

Presentation Structure Background –The Degrees of Freedom Problem –Motor Synergies Experiments in Directional Pointing –Inspiration –Model –Results Conclusion

1.) Bernstein, the Degrees of Freedom Problem and Motor Synergies Picture from Bernstein (1967)

The Degrees of Freedom Problem Nicolas Bernstein (English:1967) –Physiology of Activity –Biomechanics The DoF Problem: –“Cartesian Puppeteer”-view –Countless number of motor units –Simultaneous Control DoF Picture from Turvey et. Al. (1982)

Motor Equivalence and Context- Conditioned Variability Motor Equivalence –Redundancy through many degrees of freedom Context-Conditioned Variability –Anatomical (role of a muscle is context dependent) –Mechanical (commands are ignorant against motion/non-muscular forces) –Physiological (the spinal cord is not just a relay station) Picture from Turvey et. Al. (1982) Picture from Kandel et. Al. (2000) A = right hand; B = wrist immobilised; C = left hand; D = teeth; E = foot;

Bernstein’s Solution Motor Synergies: Systematic relationships between actuators (constraints) –Can form functional motor units (e.g. wheel position in a car) –Thereby reduce the degrees of freedom Skill Acquisition –First freezing degrees of freedom –Then freeing them and exploiting passive dynamics

Biological Evidence for Synergies Systematicities in kinetics/kinematics: –Different types of gaits, shooting, breathing (Overview: Tuller et. Al. 1982) –Linear relation between shoulder and elbow torque (Gottlieb et. Al. 1999) Complex behaviour as composition of synergies? Synergy between elbow and shoulder joint in a skilled marksperson Picture from Tuller et. Al. 1982

Problems with Motor Synergies Explaining the homunculus? Acquisition and maintenance of synergies Non-linearities when combining synergies “Motor coordination is not the goal but a means to achieve the goal of an action” (Weiss and Jeannerod (1998))

2.) Experiments in Directional Pointing Picture from Bernstein (1967)

Linear Synergies in Directional Pointing Gottlieb et. Al. 1997: –Pointing in the sagittal plane –Linear relation: –Systematic variation of scaling constant with pointing direction –Linear synergies learned? Zaal et. Al. 1999: –Linear Synergies are not learned, they constrain learning Hand trajectories Scaling constant Pre-reaching period Picture from Gottlieb et Al Picture from Zaal et Al. 1999

Simulated Robot Arm Controllers/Motors: –“Garden CTRNNs” with two motor neurons per degree of freedom (UC) –“Split Brain CTRNNs” with separate controllers for joints (SB) –Linear Synergy networks with one motor output and evolved scaling function (FS) –2 vs. 4 degrees of freedom Sensors: –Proprioception (joint angle) –Direction Screenshot of the simulated arm Different Controller Architectures

Evolutionary Robotics Experiments Scaling Function: Linear (FSa) or RBFN (FSb) Most severe simplifications: –Hand of 4 degrees model does not deviate from plane –No gravity Fitness: Position at endpoint –Start with 2 points, go up to 6 (additional goal once mean fitness >0.4) –The worse a trial, the more it weighs (exponential) –For comparison: all at once.

Results: Performance Differences Forcing Linear Synergy: –Quicker evolution –Better performance –Even with linear scaling function –Unclear why (local fitness analysis) Redundant DoFs –Better performance “ Split brain” CTRNN: –Negligible disadvantage

Results: Number of Degrees of Freedom Perturbations –Not applying torques –Blocking DoFs Redundant DoFs –Much more sensitive to blocking –More passive dynamics (i.e. forces mediated through environment)

Results: Evolved Synergies Evolved Behaviour –3D uses different starting position Evolution of Linear Synergy –Not in normal CTRNNs –Not in split brain CTRNNs Evolved RBFN –Behavioural diversity through displacement of peaks

3.) Conclusions Picture from Bernstein (1967)

Conclusions: Evolutionary Robotics Constraining of the search space (i.e. Motor Synergies) facilitates evolution Extension of the search space (i.e. more degrees of freedom) facilitates evolution Reshaping the fitness landscape The presented results may be task dependent (no generalisation) Inspiration from empirical research a good idea

Conclusions: Motor Synergies No definite conclusions about the role of motor synergies can be drawn No synergies without neural basis, but passive dynamics (prerequisite) played a role in evolved solution However, the findings comply with the findings by Zaal et Al. (1999): –Synergies are not learned –Synergies aid a developmental process

Problems/Future Research Experiments with Gravity Experiments with deviation of hand from plane Analysis of evolved synergies Energetic constraints Experiments to evolve constraints for ontogenetic development

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