4,093 research outputs found
Nonholonomic motion planning: steering using sinusoids
Methods for steering systems with nonholonomic constraints between arbitrary configurations are investigated. Suboptimal trajectories are derived for systems that are not in canonical form. Systems in which it takes more than one level of bracketing to achieve controllability are considered. The trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. A class of systems that can be steered using sinusoids (claimed systems) is defined. Conditions under which a class of two-input systems can be converted into this form are given
Combining Homotopy Methods and Numerical Optimal Control to Solve Motion Planning Problems
This paper presents a systematic approach for computing local solutions to
motion planning problems in non-convex environments using numerical optimal
control techniques. It extends the range of use of state-of-the-art numerical
optimal control tools to problem classes where these tools have previously not
been applicable. Today these problems are typically solved using motion
planners based on randomized or graph search. The general principle is to
define a homotopy that perturbs, or preferably relaxes, the original problem to
an easily solved problem. By combining a Sequential Quadratic Programming (SQP)
method with a homotopy approach that gradually transforms the problem from a
relaxed one to the original one, practically relevant locally optimal solutions
to the motion planning problem can be computed. The approach is demonstrated in
motion planning problems in challenging 2D and 3D environments, where the
presented method significantly outperforms a state-of-the-art open-source
optimizing sampled-based planner commonly used as benchmark
A Discrete Geometric Optimal Control Framework for Systems with Symmetries
This paper studies the optimal motion control of
mechanical systems through a discrete geometric approach. At
the core of our formulation is a discrete Lagrange-d’Alembert-
Pontryagin variational principle, from which are derived discrete
equations of motion that serve as constraints in our optimization
framework. We apply this discrete mechanical approach to
holonomic systems with symmetries and, as a result, geometric
structure and motion invariants are preserved. We illustrate our
method by computing optimal trajectories for a simple model of
an air vehicle flying through a digital terrain elevation map, and
point out some of the numerical benefits that ensue
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