Chapter 6 - Configuration space and collision checking

Abstract

Motion planning finds an optimal continuous sequence of robot configurations (path) that can be traversed without any collision. The collision-detection algorithms take a representation of the robot and the map and detect if any pair of shapes intersects. This transforms the planning problem into a configuration space, with each point (configuration) being free or obstacle depending on whether a ghost robot placed at the configuration incurs a collision. For efficient collision detection, the space is hierarchy decomposed (space partitioning), or simpler polygons are hierarchy regressed around robot and obstacles (bounding volume hierarchy). Continuous collision checking is used to check if a robot motion is collision-free using collision checking on the volume swept, or by maintaining a list of potentially colliding obstacles (sweep and prune). The state space additionally takes the configuration space derivatives (speeds) and models for nonholonomic constraints some differential wheel drive mobile robots cannot travel sideways.