ITC: Infused Tangential Curves for Smooth 2D and 3D Navigation of Mobile Robots ^†

Navigation is an indispensable component of ground and aerial mobile robots. Although there is a plethora of path planning algorithms, most of them generate paths that are not smooth and have angular turns. In many cases, it is not feasible for the robots to execute these sharp turns, and a smooth trajectory is desired. We present 'ITC: Infused Tangential Curves' which can generate smooth trajectories for mobile robots. The main characteristics of the proposed ITC algorithm are: (1) The curves are tangential to the path, thus maintaining G 1 continuity, (2) The curves are infused in the original global path to smooth out the turns, (3) The straight segments of the global path are kept straight and only the sharp turns are smoothed, (4) Safety is embedded in the ITC trajectories and robots are guaranteed to maintain a safe distance from the obstacles, (5) The curvature of ITC curves can easily be controlled and smooth trajectories can be generated in real-time, (6) The ITC algorithm smooths the global path on a part-by-part basis thus local smoothing at one point does not affect the global path. We compare the proposed ITC algorithm with traditional interpolation based trajectory smoothing algorithms. Results show that, in case of mobile navigation in narrow corridors, ITC paths maintain a safe distance from both walls, and are easy to generate in real-time. We test the algorithm in complex scenarios to generate curves of different curvatures, while maintaining different safety thresholds from obstacles in vicinity. We mathematically discuss smooth trajectory generation for both 2D navigation of ground robots, and 3D navigation of aerial robots. We also test the algorithm in real environments with actual robots in a complex scenario of multi-robot collision avoidance. Results show that the ITC algorithm can be generated quickly and is suitable for real-world scenarios of collision avoidance in narrow corridors.