Smooth Feedback Motion Planning with Reduced Curvature

Aref Amiri; Steven M. LaValle

cs.ROApr 2, 2026

Smooth Feedback Motion Planning with Reduced Curvature

Authors: Aref Amiri, Steven M. LaValle

Organizations: The authors are with the Faculty of Information Technology and Electrical Engineering, University of Oulu, Oulu, Finland

Abstract

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.

Figures & tables

Fig. 1 : Geometric construction of valid vector fields for 2-simplex (triangle). The conical region, constructed by boundary vectors $b_{i,j}$ , illustrates the set of valid constant cell vector fields $V_{c,i}$ that satisfy the conditions of Definition 2 . The diagram visualizes the geometric constraints for face vector fields (Definition 3 ), showing the face inward normal $n_{\text{in},f}$ , the exit face outward normal $n_{x}$ , and the hyperplane normal $n_{b_{f}}$ . The dashed lines are the GVD surface.

Fig. 2 : Geometric test for expanding the star-shaped region $\mathcal{R}$ with an adjacent simplex $\Delta_{T}$ (in 2D). (Left) A valid addition where the new vertex $v_{\text{new}}$ lies within the visibility cone from $x_{g}$ (Criterion 1 ). (Right) An invalid addition where visibility is obstructed.

Environment	Metric	Baseline	Proposed Method	Improv. (%)	Win Rate (%)
Maze $(N_{G}=109,N_{P}=52045)$	Path Length	16.70 $\pm$ 10.85	12.14 $\pm$ 7.85	27.30	97.89
	Max Curvature	23.35 $\pm$ 8.66	18.38 $\pm$ 8.40	21.30	66.59
	Total Bending	602.65 $\pm$ 1664.75	94.44 $\pm$ 76.88	84.33	97.50
	Total Turning	47.28 $\pm$ 65.04	12.21 $\pm$ 9.03	74.18	99.73
	LQR Travel Time	16.70 $\pm$ 10.85	12.14 $\pm$ 7.85	27.30	97.29
	LQR Control Effort	19.59 $\pm$ 13.12	8.00 $\pm$ 4.96	59.16	98.55

TABLE I : Quantitative Comparison of Methods.

N_{G}

: Number of Goal Cells tested,

N_{P}

: Total Integral Curves evaluated.

Panel of Figure 4 — Fig. 3 : Qualitative comparison of integral curves for the baseline and proposed methods across three environments. The maximal star-shaped region is highlighted in brown. Notably, in the Bug Trap environment, Steiner points were introduced to generate closer to equilateral triangles and avoid skewed triangles.

Environment	Method	Continuity	Success Rate (%)	Total Time (s)	Path Length (m)
Sparse (Boston)	APF	$C^{0}$	0.0	N/A	N/A
	A*	$C^{0}$	100.0	$0.042\pm 0.018$	$9.823\pm 1.797$
	RRT*	$C^{0}$	100.0	$0.826\pm 0.696$	$12.491\pm 2.314$
	FPP	$C^{k}$	100.0	$3.718\pm 0.939$	9.547 $\pm$ 1.684
	Proposed	$C^{\infty}$	100.0	0.087 $\pm$ 0.003	$10.280\pm 2.219$
Maze	APF	$C^{0}$	0.0	N/A	N/A

TABLE II : Quantitative comparison of different algorithms in two different environments. Results report the mean

\pm

standard deviation.

Panel of Figure 6 — Fig. 4 : Qualitative comparison of paths for the baselines across the maze and sparse environments.

Motion Planning

Motion planning finds safe, feasible paths and trajectories for robots and vehicles amid geometric, dynamic, and task constraints.

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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/.

Abstract

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