Contributions to Trajectory Planning and Control for Industrial and Service Robotics

Abstract

This thesis describes several contributions to some classical and new problems in robotics that appear in motion and trajectory planning, motion and trajectory representation, and motion control where we suggest new algorithms for design and analysis. These tasks are considered for standard dynamic models of robotic systems in general and for several representative examples with the specific focus at the structure of the external actuation that such systems can have. In particular, we have approached the classical fully actuated dynamical model of a mechanical system and have formulated a novel problem of orbital stabilisation of its forced periodic trajectories to explore alternative solutions for high-precision path-following control designs, which are relevant for industrial applications. In solving the problem, we have suggested a new easy-to-compute set of excessive transverse coordinates for the nominal motion. Asymptotic contraction of these transverse coordinates to zeros implies asymptotic orbital stability. As a direct consequence, nontrivial extensions to ensure orbital stabilization of the classical Inverse Dynamics and PD+ controllers, which have been previously developed for reference tracking, are proposed and elaborated in details. The analytic results have required development of a new method for the analysis of orbital stability and new rules for tuning state feedback controller’s parameters. The theoretical contribution has been successfully validated in experiments on a standard industrial robot-manipulator ABB IRB140, extended with a fast prototyping interface. The results of full-scale experiments have illustrated extraordinary performances of both novel feedback control laws in path-following accuracy and in robustness to uncertainty in load characteristics confirming our analytical predictions. The second set of contributions is related to an investigation of the motion-planning problem for underactuated mechanical systems. In this part of the thesis, two particular benchmark examples with challenging scenarios of work are approached and explored. The first example illustrates the arguments that can be used for planning sit-down motions of a humanoid robot using incentives gained from analysis of recorded human behaviours. While the another example discusses steps in planning 3-D brachiation for a gorilla robot. In both cases, the system’s models have had at least one passive degree of freedom in an ankle joint for a humanoid robot and in a hand, on which the gorilla robot hangs during brachiation, respectively. They define non-integrable constraints that must hold for any feasible for the model behaviours making the process of motion planning quite nontrivial. We have proposed and analysed procedures for feasible motion’s representation to meet dynamical constraints and heuristics, as well as arguments for choosing performance indexes and steps in efficient numerical realisations of the algorithms.