Geometric and Numerical Foundations of Movements 123

Humans out-perform contemporary robots despite vastly slower ‘wetware’ (e.g. neurons) and ‘hardware’ (e.g. muscles). The basis of human sensorymotor performance appears to be quite different from that of robots. Human haptic perception is not compatible with Riemannian geometry, the foundation of classical mechanics and robot control. Instead, evidence suggests that human control is based on dynamic primitives, which enable highly dynamic behavior with minimal highlevel supervision and intervention. Motion primitives include submovements (discrete actions) and oscillations (rhythmic behavior). Adding mechanical impedance as a class of dynamic primitives facilitates controlling physical interaction. Both motion and interaction primitives may be combined by re-purposing the classical equivalent electric circuit and extending it to a nonlinear equivalent network. It highlights the contrast between the dynamics of physical systems and the dynamics of computation and information processing. Choosing appropriate task-specific impedance may be cast as a stochastic optimization problem, though its solution remains challenging. The composability of dynamic primitives, including mechanical impedances, enables complex tasks, including multi-limb coordination, to be treated as a composite of simpler tasks, each represented by an equivalent network. The most useful form of nonlinear equivalent network requires the interactive dynamics to respond to deviations from the motion that would occur without interaction. That suggests some form of underlying geometric structure but which geometry is induced by a composition of motion and interactive dynamic primitives? Answering that question might pave the way to achieve superior robot control and seamless human-robot collaboration.