FDSPC: Fast and Direct Smooth Motion Planning via Continuous Curvature Integration

In recent decades, mobile robot motion planning has seen significant advancements. Both search-based and sampling-based methods have demonstrated capabilities to find feasible solutions in complex scenarios. Mainstream path planning algorithms divide the map into occupied and free spaces, considering only planar movement and ignoring the ability of mobile robots to traverse obstacles in the $z$-direction. Additionally, paths generated often have numerous bends, requiring additional smoothing post-processing. In this work, a fast, and direct motion planning method based on continuous curvature integration that takes into account the robot's obstacle-crossing ability under different parameter settings is proposed. This method generates smooth paths directly with pseudo-constant velocity and limited curvature, and performs curvature-based speed planning in complex 2.5-D terrain-based environment (take into account the ups and downs of the terrain), eliminating the subsequent path smoothing process and enabling the robot to track the path generated directly. The proposed method is also compared with some existing approaches in terms of solution time, path length, memory usage and smoothness under multiple scenarios. The proposed method is vastly superior to the average performance of state-of-the-art (SOTA) methods, especially in terms of the self-defined $\mathcal {S}_{2}$ smoothness (mean angle of steering). Furthermore, simulations and experiments are conducted on our self-designed wheel-legged robot with 2.5-D traversability. These results demonstrate the effectiveness and superiority of the proposed approach in several representative environments.