Column generation for a multitrip vehicle routing problem with time windows, driver work hours, and heterogeneous fleet

This study addresses a vehicle routing problem with time windows, accessibility restrictions on customers, and a fleet that is heterogeneous with regard to capacity and average speed. A vehicle can performmultiple routes per day, all starting and ending at a single depot, and it is assigned to a single driverwhose totalwork hours are limited.Acolumn generation algorithmis proposed.The column generation pricing subproblem requires a specific elementary shortest path problem with resource constraints algorithm to address the possibility for each vehicle performingmultiple routes per day and to address the need to set the workday’s start time within the planning horizon. A constructive heuristic and a metaheuristic based on tabu search are also developed to find good solutions.

Detection of gait perturbations based on proprioceptive information. Application to Limit Cycle Walkers

Walking on irregular surfaces and in the presence of unexpected events is a challenging problem for bipedal machines. Up to date, their ability to cope with gait disturbances is far less successful than humans': Neither trajectory controlled robots, nor dynamic walking machines (Limit CycleWalkers) are able to handle them satisfactorily. On the contrary, humans reject gait perturbations naturally and efficiently relying on their sensory organs that, if needed, elicit a recovery action. A similar approach may be envisioned for bipedal robots and exoskeletons: An algorithm continuously observes the state of the walker and, if an unexpected event happens, triggers an adequate reaction. This paper presents a monitoring algorithm that provides immediate detection of any type of perturbation based solely on a phase representation of the normal walking of the robot. The proposed method was evaluated in a Limit Cycle Walker prototype that suffered push and trip perturbations at different moments of the gait cycle, providing 100% successful detections for the current experimental apparatus and adequately tuned parameters, with no false positives when the robot is walking unperturbed.