Real-time smooth trajectory generation for nonholonomic mobile robots using Bézier curves

This paper focuses on generating smooth trajectories for a wheeled nonholonomic mobile robot using piecewise Bézier curves with properties ideally suited for this purpose. The developed algorithm generates smooth motion trajectories with C2 continuous curvature. We consider a teleoperated wheeled mobile robot in an indoor environment with ceiling cameras for operator visibility. The motion trajectory is constrained by the operator-specified via points and path width. A method to automatically generate a trajectory based on only these two inputs is proposed and demonstrated. To improve the trackability of the mobile robot, we adopted a Bézier subdivision method and inserted a quintic Bézier segment into high-curvature areas. The proposed algorithm can be used for real-time obstacle-avoidance trajectory generation because it allows trajectory subdivision and arbitrarily setting of the second derivative at the start point. Simulation and experimental results demonstrate the effectiveness of the proposed method.