PROJECT TITLE :
Homotopy-Based Divide-and-Conquer Strategy for Optimal Trajectory Planning via Mixed-Integer Programming
This paper proposes an optimal trajectory generation framework in which the world obstacle-avoidance downside is decomposed into simpler subproblems, corresponding to distinct path homotopies. In classical approaches to homotopic trajectory coming up with, trajectory designing and homotopy identification are performed simultaneously, resulting in a considerable computational burden. The main benefit of the proposed approach is the event of a methodology to enumerate and explicitly represent distinct homotopy classes before trajectory coming up with or optimization, which allow the matter to be decomposed into less complicated independent subproblems. The most contribution of the paper is twofold. The first contribution is the outline of a method for utilizing existing cell-decomposition strategies to enumerate and represent local trajectory generation problems that may be solved efficiently and independently. Furthermore, a relationship between the proposed cell-sequence illustration and homotopy categories is analyzed. The second contribution may be a computationally economical novel formulation of the trajectory optimization problem inside a cell sequence via mixed-integer quadratic programming (MIQP). Computational efficiency and increased resolution richness of the proposed approach are demonstrated through simulation studies. The proposed MIQP formulation fits into a linear model-predictive management framework with nonconvex collision-free constraints.
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