Smooth robotic path planning via a hybrid improved $$A^*$$ adaptive random search optimization and cubic spline framework

Path planning is a fundamental challenge in autonomous mobile robotics, where the raw outputs of classical grid-based planners such as \(A^*\) contain sharp turns and redundant waypoints that are unsuitable for direct execution. Tracking such unsmoothed paths with a Model Predictive Controller (MPC) on a \(100\,\text {m}\) grid produces positional errors exceeding \(10\,\text {m}\) and highly oscillatory acceleration commands, confirming the critical need for post-hoc trajectory smoothing. This paper proposes a three-stage hybrid framework: (i) an Improved \(A^*\) search with Dynamic Programming (DP) generates a globally feasible path and prunes redundant waypoints; (ii) an Adaptive Random Search Optimization (ARSO) algorithm adaptively places one control point per waypoint triplet by minimizing the deviation between the smoothed spline arc-length and the original segment length; and (iii) cubic spline interpolation enforces \(C^2\) -continuous trajectories via natural boundary conditions, without requiring gradient computation, convex decomposition, or neural network training. Validated on two benchmark occupancy-grid environments (a \(100\!\times \!100\) cell map at \(2.5\,\text {m/s}\) and a more demanding \(160\!\times \!160\) cell map at \(3.0\,\text {m/s}\) ), the smoothed reference reduces MPC tracking error by up to 100-fold: lateral deviation falls from \(3.0\,\text {m}\) on the raw pruned path to \(1.5\,\text {cm}\) on the ARSO-smoothed path, with residual errors converging to near-zero within \(10\,\text {s}\) in both scenarios. The framework is gradient-free, training-free, and directly compatible with standard occupancy-grid navigation stacks, making it practical for autonomous ground robots and aerial vehicles operating in obstacle-dense, real-time environments.