Time-optimal path following for robots with object collision avoidance using lagrangian duality

Time-optimal path following considers the problem of moving along a predetermined geometric path in minimum time while respecting system constraints. This paper focusses on time-optimal path following problems in robotics where collision must be avoided with other robots or moving obstacles. The developed method is based on the convex reformulation of the time-optimal path following problem with simplified dynamics presented in [1]. The robot and the obstacles are modelled as unions of convex polyhedra and the collision avoidance constraints are derived using Lagrangian duality. These constraints render the optimization problem non-convex. However, numerical simulations show that the resulting non-convex optimization problem can still be solved efficiently using a non-linear solver, due to the time-optimal path following formulation [1] and the proposed formulation of the collision avoidance constraints.