Imitation Learning of Avoidance Modes for Efficient Multimodal Model Predictive Control

Changyu Lee; Byung-Kwan Lee; Kanghoon Yoon

cs.ROOct 12, 2026

Imitation Learning of Avoidance Modes for Efficient Multimodal Model Predictive Control

Authors: Changyu Lee, Byung-Kwan Lee, Kanghoon Yoon

Organizations: Kongju National University · KAIST

Abstract

Multimodal model predictive control (MM-MPC) avoids local minima among moving obstacles by solving one optimal control problem (OCP) per combination of avoidance sides, so its computational cost grows exponentially with the number of decision-critical obstacles. We propose SideNet-MPC, which replaces this enumeration with a mode decision learned by imitating MM-MPC as an expert. A graph neural network is trained to predict the expert's minimum-cost mode, one avoidance side per obstacle. Its edges encode, for each obstacle pair, the gap predicted for the moment the vehicle first reaches either obstacle, so a neighbor that blocks a preferred passage can reverse the proposed side. The expert's selection rule compares its minimum-cost mode with the previously executed mode; SideNet-MPC keeps this rule and substitutes the network proposal for the minimum-cost mode. Hence at most two OCPs are solved per control period, and every applied input still comes from an OCP with control barrier function constraints rather than from the network. In $100$ seed-matched closed-loop Monte Carlo runs of mixed traffic, SideNet-MPC reaches $93\%$ of the expert's success rate and needs \SI{18.6}{ms} per control period on a single thread, 48% less than the expert's \SI{35.5}{ms} on sixteen parallel threads. In a controlled gap sweep, its proposed side reverses in the same gap interval as the expert's, whereas proposers without pairwise edges, trained on the same data, never reverse and all deadlock at the blocked gates of a deterministic scene.

Figures & tables

Panel of Figure 1 — Figure 1: Overview of SideNet-MPC. Both controllers apply the same selection rule to the previously executed mode and one challenger, and differ only in how the challenger is produced: the MM-MPC expert solves all $K=2^{N_{b}}=16$ OCPs and takes the minimum-cost mode, whereas SideNet-MPC solves only the mode proposed by the network, so at most two OCPs are solved per control period.

Panel of Figure 2 — Figure 2: Avoidance modes enumerated by the expert at one planning step. Each mode fixes the left/right side of every branch obstacle and yields one TC-CBF constrained OCP; the minimum-cost mode is shown in red. In (a) the four local optima lie in different homotopy classes.

Figure 3: SideNet, the mode proposer. The $N_{b}$ branch slots form a complete graph. A shared embedding maps each slot input $\mathbf{z}_{i}$ ( 7 ) to $\mathbf{h}_{i}$ , and each pair carries the edge features $\mathbf{e}_{ij}$ ( 8 ), including the gap $g^{*}_{ij}$ that the vehicle will meet when it reaches the pair. Two residual message-passing layers ( 11 ), with messages weighted by the learned range kernel ( 10 ), let each slot depend on its neighbors; a shared head emits one logit $\ell_{i}$ per slot, and the logit signs define the proposed mode $m^{\mathrm{nn}}$ .

Panel of Figure 4 — Figure 4: Representative initial snapshot of the collection environment.

Symbol	Value	Symbol	Value
$T_{s}$	$0.2\text{\,}\mathrm{s}$	$N$ ( $T_{h}$ )	$40$ ( $8\text{\,}\mathrm{s}$ )
$N_{b}$ / $N_{g}$	$4$ / $8$	$K$	$16$
$\gamma$	$0.20$	$\delta$	$0.5\text{\,}\mathrm{m}$
$R_{s}$	$1.2\text{\,}\mathrm{m}$	$d_{\mathrm{sens}}$	$20\text{\,}\mathrm{m}$
$c_{R}$	$2$	$r_{\max}$	$0.80\text{\,}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{/}\mathrm{s}$
$a_{\max}$	$1.0\text{\,}\mathrm{m}\mathrm{/}\mathrm{s}^{2}$	$\dot{r}_{\max}$	$1.0\text{\,}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{/}\mathrm{s}^{2}$

Table 1: Simulation and controller parameters.

Panel of Figure 5 — Figure 5: Deterministic scenes. Each subfigure shows the expert, SideNet-MPC and Slot-MLP, with the vehicle and nearby obstacles drawn every $10\text{\,}\mathrm{s}$ ; a cross marks where a run ends without arriving. The expert and SideNet-MPC take the same topology in all three scenes.

Figure 6: Side decision against the pair gap. The partner

b_{2}

is slid away from the lead obstacle

b_{1}

, varying the pair gap

g^{*}

of ( 9 ) while the ego vehicle and

b_{1}

stay fixed. Left: the branch logit

\ell_{b_{1}}

, positive for passing

b_{1}

on the right. Shading gives the expert’s minimum-cost side; the dashed and dotted vertical lines mark

w_{s}=2(R_{s}+\delta)

and the hull width

2R_{s}

. Right: the optimized trajectories of the modes proposed by SideNet (solid) and Slot-MLP (dash-dotted) at

g^{*}=0.3

1.9

3.2

and

4.2\text{\,}\mathrm{m}

, the third just below

w_{s}

. SideNet’s mode is the expert’s minimum-cost mode in all four; Slot-MLP passes

b_{1}

on the right in all four, and below

w_{s}

its plan heads into the gap and slows down in front of the pair.

	Arrival time [s]			Closing gate
Controller	Closing	Staggered	Obst. & gate	min. clear. [m]
Expert	19.8	52.0	29.4	0.57
SideNet-MPC	19.8	52.2	29.4	0.57
Slot-MLP	16.6	timeout	timeout	0.14
Slot-MLP-wide	16.6	timeout	timeout	0.14
Deep-set	16.6	timeout	29.4	0.14

Table 2: Deterministic scenes: arrival time [s], where “timeout” denotes no arrival within

150\text{\,}\mathrm{s}

. The last column is the minimum clearance on the closing gate.

Figure 7: Two Monte Carlo seeds (rows) for the expert, SideNet-MPC and Slot-MLP (columns), each row shown at the instant the encounter is decided. Each panel shows the past

5\text{\,}\mathrm{s}

of motion, the obstacles in view with their velocity arrows, and the predicted path of the mode being executed. The expert and SideNet-MPC select the same side, while Slot-MLP plans into the gap that a partner obstacle is closing, north of the expert’s route in seed

479

(top,

t=

10\text{,}\mathrm{s}

) and south of it in seed $494$ (bottom, $t=$9\text{\,}\mathrm{s}

), and collides at

12.4\text{\,}\mathrm{s}

and

11.2\text{\,}\mathrm{s}

respectively.

Controller	Succ.	Rel. SR	Threads	Time [ms]
Expert	97	1.00	16	35.5
SideNet-MPC	90	0.93	1	18.6
Slot-MLP	82	0.85	1	19.0
Slot-MLP-wide	83	0.86	1	19.2
Deep-set	80	0.82	1	19.1

Table 3: Closed-loop Monte Carlo evaluation on mixed traffic (

100

seeds, identical across controllers). Rel. SR is the success count divided by the expert’s. Time is the mean computation time per control period (Section 5.5 ), measured with the listed number of CPU threads.

Model Predictive Control

Model Predictive Control optimizes future actions with a system model, repeatedly applying the first action as new information arrives.

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Multimodal Trajectory Planning for Surface Vehicles using Turning Circle-based Control Barrier Functions

Changyu Lee

Department of Mechanical and Automotive Engineering, Kongju National University, Cheonan, 31080, Republic of Korea

Motion Planning Safe Motion Planning Robot Navigation Control Barrier Functions Dynamic Obstacle Avoidance Model Predictive Control

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This paper presents a guide path-free multimodal trajectory planning framework for autonomous surface vehicles operating in dynamic environments. The proposed method integrates model predictive control (MPC) with a turning circle-based control barrier function (TC-CBF). Unlike conventional Euclidean distance-based CBFs (ED-CBFs), which evaluate safety solely based on proximity, the TC-CBF accounts for the nonholonomic motion and finite turning capability of a surface vehicle. Its geometric formulation identifies feasible avoidance regions according to the vehicle's turning circles and generates distinct left- and right-turning avoidance modes. These modes allow the optimization solver to explore and select topologically different trajectories without relying on globally planned guide paths, as required by many conventional multimodal planning approaches. By embedding the avoidance direction directly into the safety constraint, the proposed framework alleviates the local-minimum and deadlock problems of single-mode MPC while maintaining computational efficiency. Extensive simulations involving multiple moving vessels demonstrate that the proposed method achieves higher success rates, fewer safety violations, and smaller residual violations than single-mode baselines across all tested traffic densities.

Abstract

Model Predictive Control

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