**6. References**


**21** 

*India* 

Debanik Roy

*Board of Research in Nuclear Sciences,* 

**Spatial Path Planning of Static Robots** 

Obstacle avoidance and robot path planning problems have gained sufficient research attention due to its indispensable application demand in manufacturing vis-à-vis material handling sector, such as picking-and- placing an object, loading / unloading a component to /from a machine or storage bins. Visibility map in the configuration space (*c-space*) has become reasonably instrumental towards solving robot path planning problems and it certainly edges out other techniques widely used in the field of motion planning of robots (e.g. Voronoi Diagram, Potential Field, Cellular Automata) for *unstructured environment*. The c-space mapping algorithms, referred in the paper, are discussed with logic behind their formulation and their effectiveness in solving path planning problems under various conditions imposed a-priori. The visibility graph (*v-graph*) based path planning algorithm generates the equations to obtain the desired joint parameter values of the robot corresponding to the ith intermediate location of the end - effector in the collision - free path. The developed c-space models have been verified by considering first a congested workspace in 2D and subsequently with the real spatial manifolds, cluttered with different objects. New lemma has been proposed for generating c-space maps for higher dimensional robots, e.g. having degrees-of-freedom more than three. A test case has been analyzed wherein a seven degrees-of-freedom revolute robot is used for articulation, followed by a case-study with a five degrees-of-freedom articulated manipulator (RHINO XR-3) amidst an in-door environment. Both the studies essentially involve new c-space mapping thematic in

Tomas Lozano Perez' postulated the fundamentals of Configuration Space approach and proved those successfully in spatial path planning of robotic manipulators in an environment congested with polyhedral obstacles using an explicit representation of the manipulator configurations that would bring about a collision eventually [Perez', 1983]. However, his method suffers problem when applied to manipulators with revolute joints. In contrast to rectilinear objects, as tried by Perez', collision-avoidance algorithm in 2D for an articulated two-link planar manipulator with circular obstacles have been reported also [Keerthi & Selvaraj, 1989]. The paradigm of *automatic transformation* of obstacles in the cspace and thereby path planning is examined with finer details [De Pedro & Rosa, 1992], such as *friction* between the obstacles [Erdmann, 1994]. Novel c-space computation algorithm for convex planar algebraic objects has been reported [Kohler & Spreng, 1995],

**1. Introduction** 

higher dimensions.

**Using Configuration Space Metrics** 

*Department of Atomic Energy, Government of India, Mumbai* 

