FLASH-CBF-RRT: Fast Lipschitz-Adaptive Safe Horizon CBF Steering for Certified Motion Planning

Safety-aware motion planning remains a challenge in robotics, especially when missions are time-critical and are under complex specifications. In this paper, we propose safety-aware-stl-mppi, a computationally efficient sampling-based receding-horizon planning framework designed to promote satisfaction of constraints expressed in Signal Temporal Logic (STL). Our approach encodes discrete-time STL formulas into candidate time-varying control barrier functions (CBF), which are integrated into a model predictive path integral (MPPI) controller. Our method inherits the benefits of low computational cost from an efficiently parallelizable sampling based planner and utilizes CBF for constraints expressed in STL. We compare against several MPPI baselines using four artificial Mars Rover planning case studies with a diverse environment and cost setups, where we show our method consistently achieving high safety and efficiency. We show a quadcopter planning experiment with NVIDIA Isaac Lab.

Feedback motion planning over cell decompositions provides a robust method for generating collision-free robot motion with formal guarantees. However, existing algorithms often produce paths with unnecessary bending, leading to slower motion and higher control effort. This paper presents a computationally efficient method to mitigate this issue for a given simplicial decomposition. A heuristic is introduced that systematically aligns and assigns local vector fields to produce more direct trajectories, complemented by a novel geometric algorithm that constructs a maximal star-shaped chain of simplexes around the goal. This creates a large ``funnel'' in which an optimal, direct-to-goal control law can be safely applied. Simulations demonstrate that our method generates measurably more direct paths, reducing total bending by an average of 91.40% and LQR control effort by an average of 45.47%. Furthermore, comparative analysis against sampling-based and optimization-based planners confirms the time efficacy and robustness of our approach. While the proposed algorithms work over any finite-dimensional simplicial complex embedded in the collision-free subset of the configuration space, the practical application focuses on low-dimensional ($d\le3$) configuration spaces, where simplicial decomposition is computationally tractable.

We propose ST-pRRTC, a GPU-parallel space- time RRT-Connect motion planner for problems with known obstacle trajectories and unspecified arrival time. Searching over many arrival times broadens temporal coverage but divides a finite planning budget among more backward trees. To address the challenge, ST-pRRTC builds a shared forward tree and an adaptive forest of backward goal-time trees. Its interval root formulation samples goal arrival times continuously and guarantees probabilistic completeness and asymptotic arrival- time optimality under the stated assumptions in a bounded time domain. The practical root recycling policy has no such guar- antees. It adapts a fixed number of backward trees, replacing later roots while retaining useful search progress. Experiments on three dynamic benchmarks show that both variants achieve lower mean first-solution times and earlier mean final arrivals than ST-RRT* and SI-RRT on problems solved by all compared methods. Further experiments demonstrate the benefit of recy- cling over broad arrival-time ranges. Real-robot demonstrations show root-recycling ST-pRRTC planning motions for a UR5e among moving Crazyflie quadrotors.