On-line Planning for Collision Avoidance on the Nominal Path

In this paper a solution to the obstacle avoidance problem for a mobile robot moving in the two-dimensional Cartesian plane is presented. The robot is modelled as a linear time-invariant dynamic system of finite size enclosed by a circle and the obstacles are modelled as circles travelling along rectilinear trajectories. This work deals with the avoidance problem when the obstacles move in known trajectories. The robot starts its journey on a nominal straight line path with a nominal velocity. When an obstacle is detected to be on a collision course with the robot, the robot must devise a plan to avoid the obstacle whilst minimising a cost index defined as the total sum squared of the magnitudes of the deviations of its velocity from the nominal velocity. The planning strategy adopted here is adjustment of the robot's velocity on the nominal path based on the time of collision between the robot and a moving obstacle, and determination of a desired final state such that its Euclidean distance from the nominal final state is minimal. Obstacle avoidance by deviation from the nominal path in deterministic and random environments is based on the work presented here and is investigated in another paper.