Motion planning for underactuated manipulators

Acknowledgments This thesis is submitted in partial fulfillment of the requirements for the degree ir. an M.Sc.at the Eindhoven University of Technology, faculty of mechanical engineering, section systems and control. First of all I would like to thank my coach and supervisor, Edo Aneke and Henk Nijmeijer for their patience and help during the project. Thanks also go out to the many people who have helped me solve so many (litte and bigger) problems along the way. Some of these people I want to mention explicitly here: Aart-Jan for his help on the H-drive and for supplying the controllers I needed, Ron Hensen for learning me to use the dSpace system and David Lizarraga for explaining me all kinds of things about Lie Brackets and controllability. Graduating appeared to be something different than the rest of my study. Whereas the first five years went by without any problems, the graduation project demanded something extra. Summary A manipulator is a a set of links connected by joints to each other and to an inertial system. Manipulators are widely used in industry and scientific environments. On a conventional manip-ulator every joint is actuated. An underactuated manipulator, however, has less actuators than joints. The advantages are apparent: cost and weight are saved. In this study underactuated manipulators are considered with one unactuated joint. The zero force or torque constraint at the unactuated joint implements a nonholonomic constraint on the system. For some underactuated manipulators the system remains controllable, despite the unactuated joint. This means these manipulators can still execute pick-and-place like tasks. These underactuated manipulators can despite of their controllability not be steered from an initial configuration to a final configuration for every arbitrary trajectory. This trajectory has to satisfy the nonholonomic constraint at every time. Motion planning for underactuated manipulators is about finding such a trajectory. In this project the underactuated PPR manipulator is considered. The dynamic equations of this system can be transformed to a simpler system, the extended chained form system. The less complex equations of the extended chained form system can help developing motion planners more easily. Three different motion planning methods are developed during the project. Each of these methods is tested in a simulated environment for motion planning problems on the PPR manipulator, to prove they work and to compare the results of different motion planners for specific motion planning problems. Finally experiments are conducted on an …