LAUSR

Optimal motion planning is one of the most critical problems in mobile robotics. On the one hand, classical sampling-based methods propose asymptotically optimal solutions to this problem. However, these planners cannot achieve smooth and short trajectories in reasonable calculation time. On the other hand, optimization-based methods are able to generate smooth and plain trajectories in a variety of scenarios, including a dense human crowd. However, modern optimization-based methods use the precomputed signed distance function for collision loss estimation, and it limits the application of these methods for general configuration spaces, including a differential drive non-circular robot with non-holonomic constraints. Moreover, optimization-based methods lack the ability to handle U-shaped or thin obstacles accurately. We propose to improve the optimization methods in two aspects. Firstly, we developed an obstacle neural field model to estimate collision loss; training this model together with trajectory optimization allows improving collision loss continuously, while achieving more feasible and smoother trajectories. Secondly, we forced the trajectory to consider non-holonomic constraints by adding Lagrange multipliers to the trajectory loss function. We applied our method for solving the optimal motion planning problem for differential drive robots with non-holonomic constraints, benchmarked our solution, and proved that the novel planner generates smooth, short, and plain trajectories perfectly suitable for a robot to follow, and outperforms the state-of-the-art approaches by 25% on normalized curvature and by 75% on the number of cusps in the MovingAI environment.