GPU-Assisted Collision Avoidance for Trajectory Optimization : Parallelization of Lookup Table Computations for Robotic Motion Planners Based on Optimal Control

Sammanfattning: One of the biggest challenges associated with optimization based methods forrobotic motion planning is their extreme sensitivity to a good initial guess,especially in the presence of local minima in the cost function landscape.Additional challenges may also arise due to operational constraints, robotcontrollers sometimes have very little time to plan a trajectory to perform adesired function. To work around these limitations, a common solution is tosplit the motion planner into an offline phase and an online phase. The offlinephase entails computing reference trajectories for varying parameterizationsof the task space in the form of a lookup table. During the online phase,a stripped down version of the optimizer is supplied with a suitable initialguess from the lookup table using the current state estimate of the robot andits surrounding bodies. This method helps in alleviating problems related toboth local minima and operational time constraints, by seeding the optimizerwith a suitable initial guess that allows it to converge to the global minimummuch faster.The problem however, shifts to the computational complexity of computinga lookup table of reference trajectories for a fine enough discreti- zation ofthe input state space. For many robotic scenarios of interest, it is oftenimpractical and sometimes computationally infeasible to compute a look uptable using a serial, single core implementation of the offline phase of a motionplanner. The main contribution of this work is to develop and evaluate amethod for reducing the time spent on computing a lookup table of referencetrajectories during the offline phase of motion planners based on optimalcontrol. We implement a method to offload the computation of collisionavoidance constraints during trajectory optimization on a Graphics ProcessingUnit (GPU), while simultaneously benefiting from a task based approach todistribute lookup table computations for independent subsets of the input statespace across multiple processes on a cluster of machines. We demonstrate theefficacy of the proposed method in a practical setting by implementing andevaluating it within a representative motion planner based on optimal control.We observe that the implemented method is 115x faster than the originalserial version of the planner, using 86 processes on 5 machines with standardserver grade hardware and 5 Graphics Processing Units in total. Additionally,we observe that the implemented method results in solutions identical to theoriginal serial version in 96.6% of cases, lending credibility for its use inrobotic motion planning.