In this paper, we introduce a generalized continuous collision detection (CCD) framework for the mobile robot along the polynomial trajectory in cluttered environments including various static obstacle models. Specifically, we find that the collision conditions between robots and obstacles could be transformed into a set of polynomial inequalities, whose roots can be efficiently solved by the proposed solver. In addition, we test different types of mobile robots with various kinematic and dynamic constraints in our generalized CCD framework and validate that it allows the provable collision checking and can compute the exact time of impact. Furthermore, we combine our architecture with the path planner in the navigation system. Benefiting from our CCD method, the mobile robot is able to work safely in some challenging scenarios.

• The authors would like to thank the editors and anonymous reviewers for their valuable feedback. 

• The authors also thank Mr. Tianyu Liu, Mr. Hongkai Ye, Dr. Shuai Zhang, and Dr. D. TM Lau for meaningful discussions.

• This work was supported by HKSAR Research Grants Council (RGC) General Research Fund (GRF) HKU 11202119, 11207818, and the Innovation and Technology Commission of the HKSAR Government under the InnoHK initiative.