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The main objective of this paper is to provide a tool for performing pathplanning at the servo level of a mobile robot. The ability to perform, in aprovably correct manner, such a complex task at the servo level can lead to alarge increase in the speed of operation, low energy consumption and highquality of response. Planning has been traditionally limited to the high levelcontroller of a robot. The guidance velocity signal from this stage is usuallyconverted to a control signal using what is known as an electronic speedcontroller (ESC). This paper demonstrates the ability of the harmonic potentialfield (HPF) approach to generate a provably correct, constrained, well behavedtrajectory and control signal for a rigid, nonholonomic robot in a stationary,cluttered environment. It is shown that the HPF based, servo level planner canaddress a large number of challenges facing planning in a realistic situation.The suggested approach migrates the rich and provably correct properties of thesolution trajectories from an HPF planner to those of the robot. This isachieved using a synchronizing control signal whose aim is to align thevelocity of the robot in its local coordinates, with that of the gradient ofthe HPF. The link between the two is made possible by representing the robotusing what the paper terms separable form. The context-sensitive andgoal-oriented control signal used to steer the robot is demonstrated to be wellbehaved and robust in the presence of actuator noise, saturation anduncertainty in the parameters. The approach is developed, proofs of correctnessare provided and the capabilities of the scheme are demonstrated usingsimulation results.

A Harmonic Potential Field Approach for Joint Planning & Control of a Rigid, Separable Nonholonomic, Mobile Robot