J Intell Robot Syst (2008) 53:223–245 DOI 10.1007/s10846-008-9239-0 Motion Planning for Haptic Guidance Jan Rosell · Carlos Vázquez · Alexander Pérez · Pedro Iñiguez Received: 14 October 2007 / Accepted: 11 April 2008 / Published online: 22 May 2008 © Springer Science + Business Media B.V. 2008 Abstract Haptic devices allow a user to feel either reaction forces from virtual inter- actions or reaction forces reflected from a remote site during a bilateral teleoperation task. Also, guiding forces can be exerted to train the user in the performance of a virtual task or to assist him/her to safely teleoperate a robot. The generation of guiding forces relies on the existence of a motion plan that provides the direction to be followed to reach the goal from any free configuration of the configuration space (C -space). This paper proposes a method to obtain such a plan that interleaves a sampling-based exploration of C -space with an efficient computation of harmonic functions. A deterministic sampling sequence (with a bias based on harmonic func- tion values) is used to obtain a hierarchical cell decomposition model of C -space. A harmonic function is iteratively computed over the partially known model using a novel approach. The harmonic function is the navigation function used as motion plan. The approach has been implemented in a planner (called the Kautham planner) that, given an initial and a goal configuration, provides: (a) a channel of cells connecting the cell that contains the initial configuration with the cell that contains the goal configuration; (b) two harmonic functions over the whole C -space, one that guides motions towards the channel and another that guides motions within the channel towards the goal; and (c) a path computed over a roadmap built with the free samples of the channel. The harmonic functions and the solution path are then used to generate the guiding forces for the haptic device. The planning approach is illustrated with examples on 2D and 3D workspaces. Keywords Haptic guidance · Feedback motion planning · Sampling-based methods · Deterministic sampling · Harmonic functions This work was partially supported by the CICYT projects DPI2005-00112 and DPI2007-63665. J. Rosell (B ) · C. Vázquez · A. Pérez Institute of Industrial and Control Engineering (IOC-UPC), Barcelona, Spain e-mail: jan.rosell@upc.edu P. Iñiguez Department of Electronics, Electrics and Automatic Engineering (URV), Tarragona, Spain