D. Kontny and O. Stursberg, “Online Adaption of Motion Paths to Time-Varying Constraints using Homotopies,” IFAC-PapersOnLine, vol. 50, no. 1, pp. 3331–3337, 2017.



This paper presents a method for optimal point-to-point control of linear discrete-time systems with time-varying non-convex state constraints, as arising for problems of avoiding moving obstacles. While common approaches like MPC with mixed-integer programming (MIP) can quickly become time-demanding, the presented approach efficiently computes circumventing near-optimal trajectories by using homotopy properties. In a first step, a range of offline selected trajectories is used to span a region of homotopic trajectories, for which the transitioning behavior between these is determined by semi-definite programming (SDP). The online part then determines with low computational effort a collision-free and near-optimal homotopic trajectory. The procedure maps the moving obstacles for relevant collision-critical time steps into the homotopy space, and determines a suitable trajectory by a tree-search of moderate size. The circumventing trajectories and the resulting computation times are illustrated by simulation.



 AUTHOR={D. Kontny and O. Stursberg},
 TITLE={{Online Adaption of Motion Paths to Time-Varying Constraints Using Homotopies}},
 BOOKTITLE={Proc. 20th IFAC World Congress},
 COMMENT={noch nicht gemeldet, ISBN: ?, ? Normseiten}}