NFOMP: Neural Field for Optimal Motion Planner of Differential Drive Robots With Nonholonomic Constraints

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.