  This article extends the capabilities of the harmonic potential field
approach to planning to cover both the kinematic and dynamic aspects of a robot
motion. The suggested approach converts the gradient guidance field from a
harmonic potential to a control signal by augmenting it with a novel type of
damping forces called nonlinear, anisotropic, damping forces. The combination
of the two provides a signal that can both guide a robot and effectively manage
its dynamics. The kinodynamic planning signal inherits the guidance
capabilities of the harmonic gradient field. It can also be easily configured
to efficiently suppress the inertia-induced transients in the robot trajectory
without compromising the speed of operation. The approach works with
dissipative systems as well as systems acted on by external forces without
needing the full knowledge of the system dynamics. Theoretical developments and
simulation results are provided in this article.
