Interpolation and optimal motion planning for mechanical systems
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Abstract
During the past few years, researchers have considered various motion planning
problems for systems with nonintegrable constraints. The aim of this thesis is to
formulate and study the problem of motion planning for systems with both complex
dynamics and nonholonomic constraints and to develop a theory of optimal
motion control for such systems. Both the kinematics and dynamics of kinematically
constrained systems present challenges. The presence of payloads with complex internal
dynamics further complicates matters. In principle, solutions can always be
found. The numerical solutions of the optimal control problems under consideration
turn out to be computationally difficult, although numerical solutions can be
found for very special boundary conditions. For low dimensional kinematic optimal
control problems, we present the optimal paths and analyze their geometry in detail.
These results contribute to the growing body of knowledge concerning explicitly
solvable motion control problems. For more general classes of problems, we appeal
to interpolation strategies. While it is relatively simple to find motions within suitably
restricted classes of interpolating functions, it is necessary to understand how far such solutions are from optimality with respect to some reasonable criterion.
Specifically, polynomial interpolants work very well when applied carefully to the
mechanical systems considered in this thesis. In addition: the methods we propose:
result in near optimal trajectories which can be readily computed and used in real
time applications.
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This work is being made available in OpenBU by permission of its author, and is available for research purposes only. All rights are reserved to the author.