GCS-Bridging: Restoring Connectivity of Disconnected Convex Sets for Graph-of-Convex-Sets Motion Planning

Xiaokai Zhou; Baoshi Cao; Yang Liu; Kui Sun; Boyu Ma; Zhengpu Wang; Zongwu Xie

cs.ROAug 23, 2026

GCS-Bridging: Restoring Connectivity of Disconnected Convex Sets for Graph-of-Convex-Sets Motion Planning

Authors: Xiaokai Zhou, Baoshi Cao, Yang Liu, Kui Sun, Boyu Ma, Zhengpu Wang, Zongwu Xie

Organizations: State Key Laboratory of Robotics and Systems, Harbin Institute of Technology, Harbin 150080 Heilongjiang Province, China. · School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore

Abstract

Graph-of-Convex-Sets (GCS)-based trajectory optimization represents collision-free regions in configuration space as a finite collection of convex sets and directly performs collision-free trajectory planning over these sets, substantially simplifying the planning process. However, existing GCS-based trajectory planning methods generally assume sufficient connectivity among the convex regions and do not explicitly address cases in which the start and goal regions belong to different connected components of the initial GCS map. To address this limitation, we propose GCS-Bridging, which reconnects disconnected convex regions through collision-free point paths followed by convex region inflation, thereby recovering the feasibility of otherwise disconnected GCS planning problems. Extensive simulations across multiple IRIS-related algorithms and scenarios demonstrate that GCS-Bridging restores missing start-to-goal connectivity in the initial GCS map with a 99.8% success rate. In addition, a hardware experiment on a single-arm Franka platform in a real-world scenario with initially disconnected start and goal regions validates the effectiveness of the proposed method in practical motion planning. Project website: https://zhouxk1997.github.io/GCS_Bridging/

Figures & tables

Fig. 1: A conceptual illustration of GCS-Bridging in an abstract configuration space. (a) Initialization is first performed in a fully known environment using multiple IRIS-related algorithms. (b) An offline GCS map is then constructed, in which the regions containing the start and goal configurations may be disconnected. The connected components and the relationships among all regions are subsequently computed from the GCS map. (c) Based on the global connectivity information of the GCS map, the algorithm attempts to locally reconnect the closest regions pair while ensuring that the entire reconnection path remains collision-free. (d) BinaryInflation is then performed along the path; once the two disconnected regions are reconnected, only the shortest connection is retained.

Region Generator	$N^{\text{init}}_{\bm{R}}\to N^{\text{final}}_{\bm{R}}$	$N^{\text{init}}_{\bm{V}}\to N^{\text{final}}_{\bm{V}}$	$T_{\text{inflate}}$ (min)	GCS-Bridging Iteration Times [O,R,I]	Total $T_{\text{bridge}}$ (min) [R+I+C]	GCSTrajOpt Cost & Result
IRIS-NP [ 14 ]	24 $\to$ 30	8 $\to$ 1	507.70	5,14,5	3.13+159.85+0.92	23.94, click here
IRIS-NP2 [ 22 ]	24 $\to$ 28	6 $\to$ 1	180.35	4,7,4	0.73+106.40+0.20	19.26 , click here
IRIS-ZO [ 22 ]	25 $\to$ 87	17 $\to$ 1	20.82	16,102,28	35.65+110.19+83.53	34.29, click here
IRIS-ZO-CUDA	25 $\to$ 90	18 $\to$ 1	2.28	17,57,28	22.75+24.91+116.39	31.34, click here

TABLE I: Comparison of GCS-Bridging using different IRIS inflation algorithms in the same dual-arm planning scenario.

Fig. 2: Multiple randomized test scenarios. Scenarios (a)–(d) are single-arm scenarios, while (e) and (f) are dual-arm scenarios. The single-arm scenarios are randomized using the framework in work [ 2 ] , with 100 trials conducted for each scenario. The dual-arm scenarios are randomized by us, with 50 trials conducted for each scenario. In (e), three colors indicate three distinct goals in the sequence solid $\rightarrow$ green $\rightarrow$ yellow $\rightarrow$ red. In (f), two colors distinguish the visually overlapping goals of the left and right arms.

Robot Type	Scenario	Reconnection Method	$N^{\text{init}}_{\bm{R}}$ $[\text{mean$ \pm $std}]$	$N^{\text{init}}_{\bm{V}}$ $[\text{mean$ \pm $std}]$	$\Delta N_{\bm{R}}$ $[\text{mean,[Q1,Q3]}]$	Success/ Trials	Reconnection Time (s) $[\text{median,[Q1,Q3],P95}]$
Single Arm	(a) Cage	DirectLine			7.06,[5.00,9.00]	77/97	14.98,[11.73,18.57],25.80
		RRT-C	$\text{18.74}\pm\text{7.98}$	$\text{5.94}\pm\text{1.46}$	9.74,[7.00,11.00]	97/97	30.21,[14.56,37.43],42.47
		Hybrid			8.46,[6.00,10.00]	97/97	17.81,[14.23,24.11],76.24
	(b) Box	DirectLine			2.93,[2.00,3.00]	93/100	21.31,[18.71,25.69],33.77
		RRT-C	$\text{15.21}\pm\text{6.17}$	$\text{5.94}\pm\text{1.53}$	3.30,[3.00,4.00]	100/100	10.20,[9.02,12.09],15.39
		Hybrid			3.05,[3.00,3.00]	100/100	21.66,[19.00,25.80],34.47

TABLE II: Random comparison of different GCS reconnection strategies in single-arm and dual-arm planning scenarios.

Fig. 3: In the hardware experiment, the Franka Panda manipulator executes collision-free planning in the sequence solid $\to$ green $\to$ yellow $\to$ red shown in (a). The primary challenge is that the configurations represented by green and red are difficult to connect directly and therefore require reconnection through GCS-Bridging. The entire experimental execution in (b) remains collision-free. Simulation result is available here , and hardware results are provided in Video 1 and Video 2 .

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Motion planning problems such as collision-free navigation and contact-rich manipulation can be naturally formulated as optimization problems that couple discrete decisions with continuous trajectories. The Graphs of Convex Sets (GCS) framework offers a practical solution to these problems. It represents discrete decisions as nodes of a graph and encodes continuous trajectories in the edges connecting them. However, the resulting optimization subproblems can become computationally prohibitive for online replanning. In this work, we propose a learning-based strategy to mitigate this limitation. Specifically, we replace the costly convex relaxation step required by nominal GCS with a single forward pass through a Graph Attention Network that predicts a set of highly probable candidate paths through the graph. A lightweight ranking network then orders these candidates by their estimated trajectory cost. Evaluating them in this order, we terminate our search early while still recovering a near-optimal motion plan. We validate the resulting pipeline across diverse robotic tasks, including collision-free motion planning for a 3D quadrotor and a 7-DoF manipulator, and planning through contact for planar pushing. Across both convex and non-convex cost and constraint settings, our approach yields up to two orders of magnitude speedup over nominal GCS while maintaining a 100% success rate, at the cost of some suboptimality in the recovered solutions. Code implementations and video demonstrations can be found at https://neural-gcs.github.io/.

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