FLASH-CBF-RRT: Certified Motion Planning

Steer around obstacles. Hold safe controls longer.
FLASH-CBF-RRT combines CBF steering with certified adaptive horizons to reduce repeated geometric evaluations and QP solves.

3.82×faster than RRT-Connect

689 / 689benchmark problems solved

2.22×faster on Reachy2

Median planning-time comparisons reported in the paper.

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 achieve effective local steering but increase planning time through expensive sequential evaluations.

We accelerate CBF steering by computing a time horizon within which a CBF-filtered velocity may be applied constantly, using closed-form kinematic bounds on collision clearance. FLASH-CBF-RRT takes adaptive steering steps that are shorter near obstacles and longer in open space, reducing intermediate evaluations. Implemented as an extension of RRT-Connect in OMPL, it matches RRT-Connect’s 100% success rate across 689 MotionBenchMaker problems while reducing median planning time by 3.82×. Hardware experiments on a 17-DoF mobile manipulator demonstrate faster planning with fewer evaluations.

Why Adaptive CBF Steering?

Straight-line extensions can collide and waste samples. CBF steering redirects them around obstacles, but repeatedly solving the safety filter is expensive. A certified safe horizon lets the planner keep a filtered control for longer, without intermediate checks or QP solves.

RRT-Connect

Straight-line extensions
Reject colliding motions

CBF-RRT-Connect

Obstacle-aware steering
Repeated safety-filter evaluations

FLASH-CBF-RRT-Connect

Certified adaptive steps
Fewer safety-filter evaluations

Certified Adaptive Horizons

A certified adaptive horizon determines how long a filtered control can be applied safely. The SDF is 1-Lipschitz, so bounding a robot link’s displacement also bounds the loss of collision clearance. Keep that displacement below the initial clearance, and the entire control hold is certified.

Turn clearance into time

Bound workspace displacement throughout a constant-velocity motion. The motion is safe while the bound stays below the available clearance.

dᵢ(t) ≤ hᵢ(q₀), ∀t ∈ [0, τ]

Here dᵢ denotes displacement and hᵢ the initial collision clearance.

MotionBenchMaker Results

Evaluated on a UR5 across 689 problems in seven environments. FLASH-CBF-RRT preserves the full success rate while reducing median planning time and the number of filter evaluations.

Planner comparison · medians from Table I
Method	Solved ↑	Time (ms) ↓	Evaluations ↓	Tree nodes ↓	Path (rad) ↓
FLASH-CBF-RRT	689	4.45	298	11	10.01
RRT-Connect	689	17.00	3,597	20	13.69
CBF-RRT-Connect	689	17.24	1,119	11	9.86
No-QP	601	92.69	10,639	90	17.66
L1 (first-order bound)	689	7.45	529	11	9.87
No-QP + L2	631	12.24	682	99	17.93

Evaluations denote collision checks for RRT-Connect, integration steps for No-QP, or CBF-QP iterations; their computational costs differ. All CBF-based returned paths passed collision auditing; one RRT-Connect path did not.

What does the adaptive horizon contribute?

With the same constraint screening, the second-order horizon is 3.75× faster than fixed-step propagation and uses 3.76× fewer QP solves.

Adaptive-horizon ablation · medians
Horizon	Solved	Time (ms)	Filter evaluations
Fixed step	689	16.69	1,119
First order (L1)	689	7.45	529
Second order (ours)	689	4.45	298

Real-World Experiments

Planning in the full 17-DoF configuration space of Reachy2. An onboard RGB-D camera supplies observations for a Kernel-SDF map, and the OMPL planner coordinates the mobile base and both arms around tabletop obstacles.

Real-world motion alongside the RGB-D camera view and the RViz representation, from the supplementary presentation.

100 randomized onboard planning queries · medians from Table II
Method	Solved	Time (ms) ↓	Evaluations ↓	Arm motion (rad) ↓
FLASH-CBF-RRT	100 / 100	12.21	206.5	1.675
RRT-Connect	100 / 100	27.05	856.5	1.973

BibTeX

Coming soon.

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