Optimal path planning for a class of nonholonomic systems with drift -

Abstract

For a system to be completely autonomous, many subsystems need to interact and ensure that the system executes the required tasks without any human intervention or guidance. One subsystem that computes the trajectory which an autonomous agent should traverse while going from an initial configuration to a predetermined final configuration is an essential part to ensure complete autonomy. Solving the path planning problem is a major research area in the field of autonomous robotics. Researchers tend to use simplified kinematic models to obtain solutions, frequently analytic, for the planned trajectories of autonomous agents. This thesis introduces a new kinematic model to describe the planar motion of an Autonomous Underwater Vehicle (AUV) moving in constant current flows. The AUV is modeled as a rigid body moving at maximum attainable forward velocity with symmetric bounds on the control input for the turning rate. The model incorporates the effect a flow will induce on the turning rate of the AUV due to the non-symmetric geometry of the vehicle. The model is then used to characterize and construct the minimum time paths that take the AUV from a given initial configuration to a final configuration in the plane. Two algorithms for the time-optimal path synthesis problem are also introduced along with several simulations to validate the proposed method. After that the assumption of maximum forward velocity is relaxed. Then a new type of paths is investigated. The trajectories computed allow the system to travel between two predetermined configurations while minimizing the total power consumption. Finally, the results are obtained numerically and geometric interpretations are presented.