High-dimensional underactuated motion planning via task space control

Kinodynamic planning algorithms have the potential to find feasible control trajectories which accomplish a task even in very nonlinear or constrained dynamical systems. Underactuation represents a particular form of a dynamic constraint, inherently present in many machines of interest (e.g., walking robots), and necessitates planning for long-term control solutions. A major limitation in motion planning techniques, especially for real-time implementation, is that they are only practical for relatively low degree-of-freedom problems. Here we present a model-based dimensionality reduction technique based on an extension of partial feedback linearization control into a task-space framework. This allows one to plan motions for a complex underactuated robot directly in a low-dimensional task-space, and to resolve redundancy with lower-priority tasks. We illustrate the potential of this approach with an extremely simple motion planning system which solves the swing-up problem for multi-link underactuated pendula, and discuss extensions to the control of walking.