2013, Feyeux, Nelson, Landry, Chantal

An algorithm to detect collisions between robots moving along given trajectories is presented. The method is a combination of the adaptive dynamic collision checking developed by Schwarzer et al. and Lin and Cannys algorithm, which computes efficiently the distance between two polyhedra. The resulting algorithm is part of a global model that computes the optimal task assignment, sequencing and kinodynamic motion planning in a robotic work-cell.

2011, Gerdts, Matthias, Henrion, René, Hömberg, Dietmar, Landry, Chantal, Maurer, Helmut

An optimal control problem to find the fastest collision-free trajectory of a robot surrounded by obstacles is presented. The collision avoidance is based on linear programming arguments and expressed as state constraints. The optimal control problem is solved with a sequential programming method. In order to decrease the number of unknowns and constraints a backface culling active set strategy is added to the resolution technique.

2013, Landry, Chantal, Welz, Wolfgang, Henrion, René, Hömberg, Dietmar, Skutella, Martin

A workcell composed of a workpiece and several welding robots is considered. We are interested in minimizing the makespan in the workcell. Hence, one needs i) to assign tasks between the robots, ii) to do the sequencing of the tasks for each robot and iii) to compute the fastest collisionfree paths between the tasks. Up to now, task assignment and path-planning were always handled separately, the former being a typical Vehicle Routing Problem whereas the later is modelled using an optimal control problem. In this paper, we present a complete algorithm which combines discrete optimization techniques with collision detection and optimal control problems efficiently

2013, Landry, Chantal, Welz, Wolfgang, Gerdts, Matthias

A new approach to find the fastest trajectory of a robot avoiding obstacles, is presented. This optimal trajectory is the solution of an optimal control problem with kinematic and dynamics constraints. The approach involves a direct method based on the time discretization of the control variable. We mainly focus on the computation of a good initial trajectory. Our method combines discrete and continuous optimization concepts. First, a graph search algorithm is used to determine a list of via points. Then, an optimal control problem of small size is defined to find the fastest trajectory that passes through the vicinity of the via points. The resulting solution is the initial trajectory. Our approach is applied to a single body mobile robot. The numerical results show the quality of the initial trajectory and its low computational cost.