Spline Path Following for Redundant Mechanical Systems

Abstract

Path following controllers make the output of a control system approach and traverse a pre-specified path with no apriori time parametrization. In this paper we present a method for path following control design applicable to framed curves generated by splines in the workspace of kinematically redundant mechanical systems. The class of admissible paths includes self-intersecting curves. Kinematic redundancies are resolved by designing controllers that solve a suitably defined constrained quadratic optimization problem. By employing partial feedback linearization, the proposed path following controllers have a clear physical meaning. The approach is experimentally verified on a 4-degree-of-freedom (4-DOF) manipulator with a combination of revolute and linear actuated links and significant model uncertainty.

A Guiding Vector-Field Algorithm for Path-Following Control of Nonholonomic Mobile Robots

“…The standard existence and uniqueness theorem [42] implies the following lemma. Proof: Reducing the Cauchy problem for the closed-loop system (25) to the Cauchy problem for (26), one shows that the solution exists locally and is unique [42]. Let its maximally prolongable solution (x(t), y(t), α(t)) be defined on ∆ * ∆ = [0; t * ) with t * < ∞.…”

“…Informally, the controller (24) provides the exponential convergence of the robot to an integral curve of the GVF; after this "fast" transient process, the robot "slowly" follows this integral curve and approaches the desired trajectory, unless it is "trapped" in a critical point. Ignoring the "fast dynamics", one may suppose that the statement of Lemma 4 remains valid for a general solution of the system (25). This argument, however, is not mathematically rigorous.…”

“…any solution starting in M remains there. (25), starting at (x(0), y(0), α(0)) ∈ M, does not leave M, and is infinitely prolongable satisfying the inequality…”

Guidance algorithm for smooth trajectory tracking of a fixed wing UAV flying in wind flows

“…If one is interested in visiting a certain area with the UAV, then it should restrict the desired trajectory P such that (23) is satisfied under the worst case condition for ||ṗ|| (determined by the expected wind speed) in (16) with η = 0. Our algorithm covers the popular splines [19] for trajectory generation in order to satisfy constraints such as (23). A conservative value for k d in order to satisfy (23) can be calculated by consideringp T Ep d = ±1 in (20).…”

Vehicle Platoon Control with Virtual Path Constraints

“…The path can also be selected to satisfy the particular application's safety requirements, as long as an appropriate diffeomorphism is defined [1][2][3][4]. Previous literature has explored different classes of paths, such as spline-interpolated paths [1,10], elliptical paths [2], and paths containing segments without curvature [11].…”