Robotic Navigation Using Harmonic Function-based Probabilistic Roadmaps.

People: Moslem Kazemi (moslemk@sfu.ca) and Mehran Mehrandezh (mehran.mehrandezh@uregina.ca)

A new hybrid robot path planning approach based on Harmonic Functions (HF) and Probabilistic Roadmaps (PRM) is presented. The proposed approach consists of building a probabilistic roadmap using information obtained about the workspace topology through the Potential Field (PF) approach based on HFs (known as harmonic potential fields). The crux of our approach is to identify narrow passages using HFs and pass them over to a PRM-like method to build a roadmap which efficiently captures the connectivity of free Configuration Space (C-space) especially in narrow regions.

 

We present two techniques to implement the proposed approach:  (1) the original Harmonic Function-based Probabilistic Roadmap (HFPRM) technique ([1]) where HFs are computed over the explicit representation of the robot's C-space, and (2) the Incremental HFPRM (IHFPRM) technique ([2]), as an extension of the original HFPRM, where no explicit representation of the C-space is required.

Original HFPRM Technique

The HFPRM technique comprises three phases: in phase one, the Laplace's equation, pertinent to the potential flow, in an environment cluttered with obstacles is solved. In phase two, a PRM with a novel sampling scheme is constructed based on the information obtained about the environment topology through the HF technique developed in phase one. The roadmap is then searched for the shortest path connecting the start and goal configurations in phase three. Promising results are obtained using this technique for solving shortest-path problem in difficult scenarios. For more details one can refer to [1].

Incremental HFPRM Technique

The IHFPRM technique works as follows: first a roadmap is initialized in robot's C-space by generating a pre-defined number of random nodes (the start and the goal configurations included). The neighboring nodes are then connected via straight lines. The metric used is the Euclidean distance. Then in an iterative scheme the roadmap is enhanced and searched for the shortest path. At each iteration the Laplace's equation, pertinent to potential flow, is solved over the current representation of the C-space using Finite Element Method (FEM) and the velocity of the flow is calculated at each node of the roadmap. The roadmap is then enhanced using a new, yet simple, random sampling scheme based on information obtained about the C-space topology with a {\it velocity thresholding} technique. This yields a roadmap with better coverage in regions associated with higher velocities (i.e. narrow regions). At the final stage the roadmap is searched by a local planner for the shortest path connecting the start and the goal configurations. The enhancement ends either after a maximum number of iterations has been reached or a collision-free path has been found. For more details one can refer to [2].

 

Inspired by the promising results obtained through the original HFPRM and incremental update of it, we present a sensor-based motion planning technique for mobile robot navigation in environments not known a priori ([3]). The main idea of the proposed technique is to utilize the information obtained through the HFs to prioritize different regions in the workspace at the scan planning stage of a sensor-based PRM. The proposed technique was implemented to navigate a real mobile robot in environments not known a priori. For more details one can refer to [3].

 

Related Publications

[1] Robotic Navigation Using Harmonic Function-based Probabilistic Roadmaps
M. kazemi, M. Mehrandezh
Proceedings of IEEE International Conference on Robotics and Automation (ICRA)
New Orleans, LA, Apr. 2004, pp. 4765-4770.

[2] An Incremental Harmonic Function-based Probabilistic Roadmap Approach to Robot Path Planning
M. Kazemi, M. Mehrandezh, K, Gupta
Proceedings of IEEE International Conference on Robotics and Automation (ICRA)
Barcelona, Spain, Apr. 2005, pp. 2148-2153

[3] Sensor-based Robot Path Planning Using Harmonic Function-based Probabilistic Roadmaps
M. Kazemi, M. Mehrandezh, K. Gupta
Proceedings of International Conference on Advanced Robotics (ICAR)
Seattle, WA, USA, July 2005, pp.84-89

[4] Robot Path Planning Using Harmonic Function-based Probabilistic Roadmaps
M. Kazemi, M. Mehrandezh, K. Gupta
Journal paper in prepration