Task-space separation principle: a force-field approach to motion planning for redundant manipulators

In this work, we address human-like motor planning in redundant manipulators. Specifically, we want to capture postural synergies such as Donders' law, experimentally observed in humans during kinematically redundant tasks, and infer a minimal set of parameters to implement similar postural synergies in a kinematic model. For the model itself, although the focus of this paper is to solve redundancy by implementing postural strategies derived from experimental data, we also want to ensure that such postural control strategies do not interfere with other possible forms of motion control (in the task-space), i.e. solving the posture/movement problem. The redundancy problem is framed as a constrained optimization problem, traditionally solved via the method of Lagrange multipliers. The posture/movement problem can be tackled via the separation principle which, derived from experimental evidence, posits that the brain processes static torques (i.e. posture-dependent, such as gravitational torques) separately from dynamic torques (i.e. velocity-dependent). The separation principle has traditionally been applied at a joint torque level. Our main contribution is to apply the separation principle to Lagrange multipliers, which act as task-space force fields, leading to a task-space separation principle. In this way, we can separate postural control (implementing Donders' law) from various types of tasks-space movement planners. As an example, the proposed framework is applied to the (redundant) task of pointing with the human wrist. Nonlinear inverse optimization (NIO) is used to fit the model parameters and to capture motor strategies displayed by six human subjects during pointing tasks. The novelty of our NIO approach is that (i) the fitted motor strategy, rather than raw data, is used to filter and down-sample human behaviours; (ii) our framework is used to efficiently simulate model behaviour iteratively, until it converges towards the experimental human strategies.