Free Space Mapping and Motion Planning in Configuration Space for Mobile Manipulators

A new method for calculating the collision free areas of a manipulator´s configuration space (C-space) is demonstrated in this paper. Rather than mapping a point obstacle to an n-dimensional surface in the C-space, the dual problem is considered. That is, regions of the C-space that are guaranteed to be collision free are determined. Whilst some configurations that are collision free are not captured by this method, its speed and low memory usage make it ideal for motion planning in the C-space. It is especially useful for mobile manipulators such as wall climbing robots, where the surrounding terrain changes with each step the robot takes. Being able to compute the mapping of Cartesian to C-space representations of objects in real time is essential, as the workspace for these robots is not static and therefore cannot be precalculated. Once the free areas of C-space have been determined, more conventional path planning techniques which have been developed for point robots moving around forbidden areas can be used for the generation of a motion plan. This means that motion planning can be guaranteed to have an exhaustive search through all possible paths and return the lowest cost path - something that has previously been difficult to achieve with other manipulator motion planning techniques. The technique is demonstrated for a 2-degree of freedom planar manipulator, and will be extended in the future to apply to higher dimensional C-spaces. Further developments are suggested for further optimisation of the technique, most notably the idea of partitioning the C-space.