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

Mani Amani; Hesam Mojtahedi; Reza Akhavian; Nikolay Atanasov; Ki Myung Brian Lee

cs.ROOct 16, 2026

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

Authors: Mani Amani, Hesam Mojtahedi, Reza Akhavian, Nikolay Atanasov, Ki Myung Brian Lee

Organizations: Department of Civil, Construction, and Environmental Engineering, San Diego State University, San Diego, CA, USA · Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, CA, USA

Abstract

Fast motion planning requires both sample-efficient exploration and computationally efficient local steering. Conventional straight-line steering is inexpensive but wastes samples by rejecting colliding extensions. Quadratic program controllers with control barrier function (CBF) constraints can be used to achieve effective local steering but can increase the planning time due to the expensive sequential evaluations. We develop a method to accelerate CBF steering by computing a time horizon within which CBF-filtered velocity may be applied constantly using closed-form kinematic bounds on collision-clearance. Our method, FLASH-CBF-RRT, significantly reduces the number of evaluations compared to prior CBF-RRT approaches because the planner can take adaptive steering step sizes that are shorter near obstacles and longer in open space. We implement this steering procedure as an extension of RRT-Connect in OMPL. Across 689 MotionBenchMaker problems, FLASH-CBF-RRT matches RRT-Connect's 100% success rate while reducing median planning time by 3.82x, and is 3.88x faster than fixed-step CBF-RRT. Hardware experiments on a 17-DoF mobile manipulator demonstrate 2.2x faster planning and 4.2x fewer evaluations. Videos and results are available at: https://mamani828.github.io/FLASH-CBF-RRT/.

Figures & tables

Fig. 1 : FLASH-CBF-RRT. (a) A CBF safety filter steers tree extensions around obstacles instead of rejecting them. Each filtered control is held for a certified duration, computed in closed form as the time at which a kinematic bound on link displacement under constant joint velocity would exhaust the current collision clearance. (b)–(c) Workspace- and configuration-space views.

Fig. 2 : Certified CBF steering. (a) One extension from

\mathbf{q}_{\mathrm{near}}

toward

\mathbf{q}_{\mathrm{rand}}

. At each orange dot, the safety filter ( 4 ) computes a control held for the certified duration

\tau_{\mathrm{hold}}

, yielding longer segments in open space and shorter segments near obstacles. (b) Control-space view at the circled configuration. Solid lines denote retained CBF constraints; the green polygon is the feasible set within the joint-velocity limits, onto which

\mathbf{u}_{\mathrm{nom}}

is projected to obtain

\mathbf{u}^{\star}

. Dashed lines denote constraints (

h_{4}

h_{5}

) certified redundant by Theorem IV.3 . (c) Workspace view with a sphere-approximated mobile manipulator and an SDF cross-section. SDF queries at sphere centers provide distances and gradients for the safety filter. Spheres 1–3 generate the retained constraints in (b); spheres 4 and 5 generate the screened constraints.

Fig. 3 : Workspace and configuration-space view of the adaptive horizon bounds at $\mathbf{q}_{0}$ . (a) The initial robot configuration, the first-order and second-order certified endpoints $\mathbf{q}_{\mathrm{Lip}}$ and $\mathbf{q}_{\mathrm{Kin}}$ , and the exact contact configuration $\mathbf{q}_{\mathrm{FK}}$ in the workspace. (b) A configuration-space view of (a), with regions showing potential hold times along other directions.

Fig. 4 : Comparison with geometric, CBF-QP, and QP-free planning. Dark-gray, blue, orange, pink, and purple curves denote RRT-C, CBF-RRT-C, No-QP, No-QP + L2, and Ours respectively. Plots show the percentage of problems solved within the planning-time, filter-evaluation, or tree-node budget.

Fig. 5 : Adaptive-step ablation on the UR5 dataset. Green, turquoise, and purple denote Fixed, L1, and Ours, respectively.

Method	Solved	Time	Nodes	Eval.	Motion	QP
		(ms)			(rad)	size
Ours	689	4.45	11	298	10.01	277.2
Baselines
RRT-C	689	17.00	20	3597	13.69	–
CBF-RRT-C [ 7 ]	689	17.24	11	1119	9.86	342.0
No-QP [ 10 ]	601	92.69	90	10639	17.66	–

TABLE I : Results across 689 scenarios. Solved: number of scenarios solved. The reported statistics are medians. Eval.: number of collision checks (RRT-C), integration steps for No-QP, or CBF-QP iterations. Nodes: number of vertices in the tree; Motion: path length in radians; QP size: number of constraints per CBF-QP solve. CBF variants all return collision-free paths, while one collision was found among RRT-C. Best values are boldfaced.

Fig. 6 : Reachy2 in the tabletop scene. Ghost poses show configurations along one planned 17-DoF motion, where the mobile base approaches the table, and both arms reach between the obstacles.

Method	Solved	Time	Nodes	Eval.	Path Length	Motion
		(ms)			(m)	(rad)
Ours	100	12.21	10	206.5	1.648	1.675
RRT-C	100	27.05	13	856.5	1.623	1.973

TABLE II : Median performance over 100 randomized onboard planning queries on a real Reachy2 mobile manipulator. Solved: no. of problems solved. Time: planning time. Eval: no. of collision checks or CBF-QP solves. Path length: base motion length. Motion: arm motion length. Goals are sampled over a mapped table, with base poses placed on a surrounding ring. Planning is performed in the full 17-DoF configuration space using a live SDF map.

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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.

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