Path Following for Mobile Manipulators

This is a post-peer-review, pre-copyedit version of an article published in Robotics Research. The final authenticated version is available online at: http://dx.doi.org/https://doi.org/10.1007/978-3-319-60916-4_30This paper presents a framework of path following via set stabilization for mobile manipulator systems. The mobile manipulator is modelled as a single redundant dynamic system. The mobile base considered belongs to a large class of wheeled ground vehicles, including those with nonholonomic constraints. Kinematic redundancies are resolved by designing a controller that solves a suitably defined constrained quadratic optimization problem, which can be easily tuned by the designer to achieve various desired poses. By employing partial feedback linearization, the proposed path following controller has a clear physical meaning. The desired path to be followed is a spline in the output space of the system. The controller simultaneously controls the manipulator and mobile base. The result is a unified path following controller without any trajectory planning performed on the mobile base. The approach is experimentally verified on a 4-degree-of-freedom (4-DOF) manipulator mounted on a differential drive mobile platfor

Adaptive Path Following for an Underactuated Nonholonomic Mobile Manipulator

We investigate an adaptive path following problem for an underactuated nonholonomic mobile manipulator system and closed planar curves. As opposed to adapting to uncertain or unknown dynamics in the plant, we apply an adaptation approach with respect to an unknown geometric path. First, we present a solution to the non-adaptive path following problem using the concept of a path following output and apply it to circular and elliptical paths. To overcome a drawback associated with our first proposed solution and set the stage for our approach to the adaptive case, we apply an approximation approach based on osculating circles for strictly convex closed curves. We transition to the adaptive path following case by first presenting an algorithm to estimate unknown path parameters in the case of a circular path. We use our estimation algorithm and our path following solution for circular paths in an indirect adaptive control scheme. Thereafter, again using the osculating circle of a curve and the approximation technique of our second non-adaptive path following solution, we extend our adaptive solution, under some mild assumptions, for unknown strictly convex closed curves in the plane

Stabilization of Polytopes for Fully Actuated Euler-Lagrange Systems

Given an Euler-Lagrange system and a convex polytope in its output space, we design a switched feedback controller that drives the output to the polytope. On the polytope, the system output tracks assigned trajectories or follows assigned paths. The study of this problem is motivated by industrial applications such as robotic painting, welding and three dimensional printing. Many engineering systems, such as robotic manipulators, can be modelled with Euler-Lagrange equations, and many engineered surfaces, designed using software, are naturally modelled as convex polytopes. We use feedback linearization to decompose the design problem into two subproblems; stabilizing the polytope surface, and controlling its motion along the surface. The first subproblem, known as the design of the transversal controller, leverages the fact that a polytope can be represented as a finite union of facets. The controller determines the closest facet to the system output and stabilizes that facet by stabilizing its corresponding hyperplane via feedback linearization. The transversal dynamics can be stabilized using linear controllers. At the boundary of a facet, we propose a switching law that ensures weak invariance of the polytope for the closed-loop system. The second subproblem, known as the design of the tangential controller, enforces desired dynamics while the system output is restricted to the polytope. We investigate control specifications such as following a predefined path on the surface and tracking a trajectory that moves along the surface. The separation of the transversal and tangential control design phases is possible because feedback linearization decouples the transversal and tangential dynamic subsystems. This approach to control design is demonstrated experimentally on a four degree-of freedom robotic manipulator. The experimental implementation is made robust to modelling uncertainty via Lyapunov re-design methods

Robust Spline Path Following for Redundant Mechanical Systems

Path following controllers make the output of a control system approach and traverse a pre-specified path with no a priori time-parametrization. The first part of the thesis implements a path following controller for a simple class of paths, based on transverse feedback linearization (TFL), which guarantees invariance of the path to be followed. The coordinate and feedback transformation employed allows one to easily design control laws to generate arbitrary desired motions on the path for the closed-loop system. The approach is applied to an uncertain and simplified model of a fully actuated robot manipulator for which none of the dynamic parameters are measured. The controller is made robust to modelling uncertainties using Lyapunov redesign. The experimental results show a substantial improvement when using the robust controller for path following versus standard state feedback. In the second part of the thesis, the class of paths and systems considered are extended. We present a method for path following control design applicable to framed curves generated by spline interpolating waypoints in the workspace of kinematically redundant mechanical systems. The class of admissible paths include self-intersecting curves. Kinematic redundancies of the system are resolved by designing controllers that solve a suitably defined constrained quadratic optimization problem that can be easily tuned by the designer to achieve various desired poses. The class of redundant systems considered include mobile manipulators for a large class of wheeled ground vehicles. The result is a path following controller that simultaneously controls the manipulator and mobile base, without any trajectory planning performed on the mobile base. The approach is experimentally verified using the robust controller developed in the first part of the thesis on a 4-degree-of-freedom (4DOF) redundant manipulator and a mobile manipulator system with a differential drive base