Robust and Energy Efficient Trajectories in a Stochastic Common Workspace Setting

A trajectory planning formulation incorporating robustness is proposed in this paper, where uncertainties in the availability of a common workspace for robots are present. By introducing a clearance point where the occupancy of the shared space is evaluated and restricting the velocity and arrival time at this point, collision free paths are guaranteed. The expected final time and energy consumption are derived and sensitivity analysis are performed to study how changes in clearance point position and arrival time impact these measures. A simulation study is presented where the stochastic time at which a common workspace becomes available follows a uniform, normal and exponential distribution. The optimal clearance point, arrival time and expected values for final time and energy consumption are obtained and compared for the different distributions. For the uniform and normal distribution, the results show that the expected final time is robust to uncertainties, while energy savings are possible for the uniform and exponential distribution when redundant time is available.