Motion Control and Planning for Nonholonomic Kinematic Chains
MARYLAND UNIV COLLEGE PARK INST FOR SYSTEMS RESEARCH
Pagination or Media Count:
In this dissertation we examine a class of systems where nonholonomic kinematic constraints are combined with periodic shape variations, giving rise to a snake-like undulating motion of the system. Within this class, we distinguish two subclasses, one where the system possesses enough kinematic constraints to allow the control of its motion to be based entirely on kinematics and another which does not in the latter case, the dynamics plays a crucial role in complementing the kinematics and in making motion control possible. An instance of these systems are the Nonholonomic Variable Geometry Truss NVGT assemblies, where shape changes are implemented by parallel manipulator modules, while the nonholonomic constraints are imposed by idler wheels attached to the assembly. We assume that the wheels roll without slipping on the ground, thus constraining the instantaneous motion of the assembly. These assemblies can be considered as land locomotion alternatives to systems based on legs or actuated wheels. Their propulsion combines features of both biological systems like skating humans and snakes and of man-made systems like orbiting satellites with manipulator arms. The NVGT assemblies can be modeled in terms of the Special Euclidean group of rigid motions on the plane. Generalization to nonholonomic kinematic chains on other Lie groups U gives rise to the notion of U-Snakes.
- Numerical Mathematics