A Geometric Approach To Path-following Motion Control

Mobile robots include underwater vehicles, ground robots, aerial robots andspace robots, their motion control can be classified into two categories: trajectorytracking and path following. Trajectory tracking is that the vehicle tracks apre-specified time-parametric curve and reaches a special point, it emphasizes boththe space consistency and the time consistency. While path following problem is thatthe vehicle tracks the geometric path of the space, it doesn’t need the timeconsistency. The error of path following (also called contour error) can’t be inflectedin the motion control models visually, which increased the difficulties in motioncontrol system design. By utilizing differential geometric approach, this thesispresents a general description for path following motion control problems. By thisway, the analytical form of contour error visualize can be given in the modeling ofthe control system. A general framework is proposed for path following motioncontrol problems.Firstly, by using a rotation matrix, this thesis transforms the path followingmotion control problem from the inertia frame to the Frenet frame, and expresses thecontour error and attitude error analytically. For the case of planar path following,the contour error can be approximated as the normal vector component in the Frenetframe, and the attitude error can be taken as the angle between the vehicle velocityvector and the tangent vector of the given path. For the case of space path following,the principal normal and subnormal vector component of the Frenet frame canapproximately be taken as the projection of the contour error, and the angularvelocity error can be regarded as the error of the anglular velocity projection in theinertia frame between body frame and Frenet frame.Based on that problem, a general control strategy is proposed for the pathfollowing motion control system, and then the path following motion control modelis transformed into chain system. We build on Lyapunov theory to choose thecontroller to reduce contour error and attitude errors to zero. For the case of planarpath following, take the differential mobile robot and front wheel steering robot asexample, we build the kinematics models of the Frenet frame, and then design thecontroller. A circle is followed by the mobile robots, their simulation results verifythe feasibility of the planar path following control strategy. For the case of spacepath following, the underwater mobile vehicle is taken as example, we build themotion control model of Frenet frame for underwater vehicle, and a nonlinearcontrol strategy is taken into account the control system. The simulation resultsshow the feasibility of the controller design.