Implementation of Nonlinear Model Predictive Path-Following Control for an Industrial Robot

Many robotic applications, such as milling, gluing, or high precision measurements, require the exact following of a pre-defined geometric path. In this paper, we investigate the real-time feasible implementation of model predictive path-following control for an industrial robot. We consider constrained output path following with and without reference speed assignment. We present results from an implementation of the proposed model predictive path-following controller on a KUKA LWR IV robot.Comment: 8 pages, 3 figures; final revised versio

Nonlinear Model Predictive Control for Constrained Output Path Following

We consider the tracking of geometric paths in output spaces of nonlinear systems subject to input and state constraints without pre-specified timing requirements. Such problems are commonly referred to as constrained output path-following problems. Specifically, we propose a predictive control approach to constrained path-following problems with and without velocity assignments and provide sufficient convergence conditions based on terminal regions and end penalties. Furthermore, we analyze the geometric nature of constrained output path-following problems and thereby provide insight into the computation of suitable terminal control laws and terminal regions. We draw upon an example from robotics to illustrate our findings.Comment: 12 pages, 4 figure

Feedback and Partial Feedback Linearization of Nonlinear Systems: A Tribute to the Elders

Arthur Krener and Roger Brockett pioneered the feedback linearization problem for control systems, that is, the transforming of a nonlinear control system into linear dynamics via change of coordinates and feedback. While the former gave necessary and sufficient conditions to linearize a system under change of coordinates only, the latter introduced the concept of feedback and solved the problem for a particular case. Their work was soon extended in the earlier eighties by Jakubczyk and Responder, and Hunt and Su who gave the conditions for a control system to be linearizable by change of coordinates and feedback (full rank and involutivity of the associated distributions). It turned out that those conditions are very restrictive; however, it was showed later that systems that fail to be linearizable can still be transformed into two interconnected subsystems: one linear and the other nonlinear. This fact is known as partial feedback linearization. For input-output systems with well-defined relative degree, coordinates can be found by differentiating the outputs. For systems without outputs, necessary and sufficient geometric conditions for partial linearization have been obtained in terms of the Lie algebra of the system; however, both results of linearization and partial feedback linearization lack practicability. Until recently, none has provided a way to actually compute the linearizing coordinates and feedback. In this paper, we propose an algorithm allowing to find the linearizing coordinates and feedback if the system is linearizable, and in the contrary, to decompose a system (without outputs) while achieving the largest linear subsystem. Those algorithms are built upon successive applications of the Frobenius theorem. Examples are provided to illustrate

Transverse Feedback Linearization with Partial Information for Single-Input Systems

“First Published in SIAM Journal on Control and Optimization in 2014, published by the Society for Industrial and Applied Mathematics (SIAM)” and the copyright notice as stated in the article itself (e.g., “Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.”')This paper is motivated by the problem of asymptotically stabilizing invariant sets in the state space of control systems by means of output feedback. The sets considered are smooth embedded in submanifolds and the class of system is nonlinear, finite-dimensional, autonomous, deterministic, single-input and control-affine. Given an invariant set and a control system with fixed output, necessary and sufficient conditions are presented for feedback equivalence to a normal form that facilities the design of output feedback controllers that stabilize the set using existing design techniques.This work was supported by supported by the National Science and Engineering Research Council (NSERC) of Canad

Coordinated path following of unicycles : A nested invariant sets approach

The final publication is available at Elsevier via http://dx.doi.org/https://doi.org/10.1016/j.automatica.2015.06.033. © 2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/We formulate a coordinated path following problem for N unicycle mobile robots as an instance of a nested set stabilization problem. Stabilization of the first set corresponds to driving the unicycles to their assigned paths. Stabilization of the second set, a subset of the first, corresponds to meeting the coordination specification. The first set is stabilized in a decentralized manner using feedback linearization. For arbitrary coordination tasks we utilize feedback linearization to stabilize the nested set in a centralized manner. In the special case in which coordination entails making the unicycles maintain a formation along their paths, we propose semi-distributed control law under less restrictive communication assumptions. Experimental results are provided

Path Following for Robot Manipulators Using Gyroscopic Forces

This thesis deals with the path following problem the objective of which is to make the end effector of a robot manipulator trace a desired path while maintaining a desired orientation. The fact that the pose of the end effector is described in the task space while the control inputs are in the joint space presents difficulties to the movement coordination. Typically, one needs to perform inverse kinematics in path planning and inverse dynamics in movement execution. However, the former can be ill-posed in the presence of redundancy and singularities, and the latter relies on accurate models of the manipulator system which are often difficult to obtain. This thesis presents an alternative control scheme that is directly formulated in the task space and is free of inverse transformations. As a result, it is especially suitable for operations in a dynamic environment that may require online adjustment of the task objective. The proposed strategy uses the transpose Jacobian control (or potential energy shaping) as the base controller to ensure the convergence of the end effector pose, and adds a gyroscopic force to steer the motion. Gyroscopic forces are a special type of force that does not change the mechanical energy of the system, so its addition to the base controller does not affect the stability of the controlled mechanical system. In this thesis, we emphasize the fact that the gyroscopic force can be effectively used to control the pose of the end effector during motion. We start with the case where only the position of the end effector is of interest, and extend the technique to the control over both position and orientation. Simulation and experimental results using planar manipulators as well as anthropomorphic arms are presented to verify the effectiveness of the proposed controller

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

Path Following and Output Synchronization of Homogeneous Linear Time-Invariant Systems

This thesis examines two aspects of the path following control design problem for Linear Time-Invariant (L.T.I.) systems assigned closed curves in their output space. In the first part of the thesis we define a path following normal form for L.T.I. systems and study structural properties related to this normal form. We isolate how unstable zero dynamics alter the feasibility of using the path following normal form for control design. In the second half of the thesis we consider a synchronized path following problem for a homogenous multi-agent system and cast the problem as an instance of an output synchronization problem to leverage recent results from the literature. It is desired that each individual agent follow a specified path. The agents communicate with one another over an idealized communication network to synchronize their positions along the path. The main result is the construction of a dynamic feedback coupling that drives all the agents in the network to their respective reference paths while simultaneously synchronizing their positions along the path. Laboratory results are presented to illustrate the effectiveness of the proposed approach

Modelling and Navigation of Autonomous Vehicles on Roundabouts

A path following controller was proposed that allows autonomous vehicles to safely navigate roundabouts. The controller consisted of a vector field algorithm that generated velocity commands to direct a vehicle. These velocity commands were fulfilled by an actuator controller that converts the velocity commands into wheel torques and steering angles that physically move a vehicle. This conversion is accomplished using an online optimization process that relies on an internal vehicle model to solve for necessary wheel torques and steering angles. To test the controller’s performance, a 16 degree of freedom vehicle dynamic model was developed with consideration for vehicle turn physics. Firstly, tire force data was gathered by performing driving maneuvers on a test track using a vehicle fitted with tire measurement equipment. The generated tire force data was used to compare various combined slip tire force models for their accuracy. The most accurate model was added to the high-fidelity vehicle model. Next, suspension kinematic data was generated using a simple testing procedure. The vehicle was equipped with the tire measurement equipment and the vehicle was raised a lowered with a hydraulic jack. Using displacement and orientation data from this test, a novel reduced order suspension kinematic model that reproduces the observed motion profile was developed. Application of the path following controller to the high-fidelity model resulted in close following of a roundabout path with small deviations