CONVEXIFICATION OF MOTION PLANNING THROUGH LIFTINGS AND HYPERCOMPLEX NUMBERS
Abstract
The goal of the proposed research is the development of a rigorous mathematical and algorithmic framework to explore the role of parameterization in complex motion planning problems for controlled dynamical systems. Specifically, we will examine how novel parameterizations of control, configuration space, and logical constraints, can be effectively utilized to develop convex optimization-based solution methods and autonomously executable algorithms for complex motion planning problems. The motion planning problems of interest have non-convex constraints due to control, state, or coupled statecontrol constraints. The classes of parameterizations of particular interest are: (1) parametrization of the control space via a lifting to ensure generalized non-singularity of the optimal trajectories leading to lossless convexification of non-convex control constraints; (2) parameterization of the configuration space using quaternions, dual-quaternions, and more generally hypercomplex numbers, facilitating convexification of otherwise non-convex state and coupled state-control constraints; (3) parameterization of a rich class of complex conditionally triggered constraints by using complementarity-type formulations to utilize continuous solution variables rather than binary ones, facilitating the use of convex optimization based solution methods, i.e., successive convexification.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2021
- Source ID
- FA95502010053
Entities
People
- Behçet Açıkmeşe
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Washington