IFAC World Congress 2026 · Busan MoC32 · JO-MECH: High-Performance Motion Control Systems 15:30 – 15:50 · Paper MoC32.1

Efficient COLREGs-Compliant Collision
Avoidance Using Turning Circle-Based
Control Barrier Function

Changyu Lee¹, Jinwook Park², Jinwhan Kim²

¹ Kongju National University, Department of Mechanical & Automotive Engineering

² KAIST, Department of Mechanical Engineering

Introduction · Research background

ASVs must avoid collisions the right way

1

Guaranteeing safety is essential for autonomous surface vehicles (ASVs)

Ships that navigate and control themselves without direct human operation

2

International regulations for preventing collisions at sea (COLREGs)

“Maritime traffic rules”

They specify how each ship must maneuver when it encounters another ship

Not only avoid collisions, but avoid them in the way COLREGs require

COLREGs-compliant evasive maneuvers

Own shipTarget ship

COLREGs evasive maneuvers of the own ship: overtaking on either side, both ships turning to starboard when head-on, and turning to starboard to pass astern in a crossing

OvertakingRule 13

Keep out of the way of the ship being overtaken

Head-onRule 14

Both ships alter course to starboard

CrossingRule 15

Give-way ship turns to starboard and passes astern

Introduction · Related work

Two existing approaches, two limitations

1

Velocity obstacle (VO)

Velocity obstacle: the own ship picks a velocity whose relative velocity to the target ship lies outside the collision cone — Existing
Choose a velocity outside the collision cone

Limit

Can result in overly conservative behavior

Limits the ship’s velocity to avoid collision in compliance with COLREGs

2

Model predictive control (MPC)

MPC-based collision avoidance: the predicted target ship motion is imposed as constraints while the own ship trajectory is optimized — Existing
Predict motion, optimize under constraints

Limit

Outperforms VO but needs more computation

An optimization problem over the prediction horizon at every step

Research objective

COLREGs-compliant collision avoidance with MPC-level performance at high computational efficiency

Introduction · Control barrier function (CBF)

A CBF keeps the system inside a safe set

CBF

Safe set and CBF constraint

Pre-defined safe set\(h(\mathbf{x})\ge 0\)

CBF constraint

\(\dot h(\mathbf{x},\mathbf{u})+\gamma\,h(\mathbf{x})\ge 0\)

for some \(\mathbf{u}\in U\), with \(\gamma>0\): \(h\) may decrease, but never faster than the exponential bound \(\dot h=-\gamma h\), so it never crosses zero.

\(\dot h=-\gamma h\) \(\dot h\ge-\gamma h\) Always stays positive: safe

Collision avoidance

Distance-based CBF

The CBF limits the speed toward an obstacle in proportion to the relative distance from it: \(-\dot h(\mathbf{x})\le\gamma\,h(\mathbf{x})\)

Introduction · Safety filter (CBF-QP)

A CBF-QP safety filter works with any controller

Nominal controllerany controller

Safety filter · CBF-QP

\[\begin{aligned}\mathbf{u}^{*}=\;&\arg\min_{\mathbf{u}\in\mathbb{R}^m}\ \|\mathbf{u}-\mathbf{u}_n\|_H^2\\ \text{s.t.}\;\;&L_f h(\mathbf{x})+L_g h(\mathbf{x})\,\mathbf{u}+\gamma\,h(\mathbf{x})\ge 0\\ &\mathbf{u}_{\min}\le\mathbf{u}\le\mathbf{u}_{\max}\end{aligned}\]

Vehicle

\(\mathbf{u}_n\) \(\mathbf{u}\)

Compatible with any controller Changes the nominal input as little as possible Computationally efficient

Challenge

How to integrate COLREGs into CBFs to ensure rule compliance and improve performance?

1

Conventional CBFs lack explicit logic for avoidance direction

In COLREGs the direction is the key point: the rules tell the ship which way to go

2

They do not properly account for ships’ turning limitations

A ship cannot turn in place

Target ship domain: a line through points p_D and p_B, defined relative to the target ship position, heading and bearing, bounds the region the own ship must stay out of — Prior work: target ship domain + CBF

Proposed method · Turning circle-based CBF (TC-CBF)

Keep the turning circles free of obstacles

Two TC-CBFs ensure safety by keeping the vehicle’s left and right turning circles, defined by its speed, heading, and turning limit, free of obstacles.

\[R=\alpha\,\frac{u}{r_{\max}}\]

Turning radius at the maximum turning rate \(r_{\max}\); the scaling factor \(\alpha\) enlarges the circle for a smoother turn

\[h_{tr}(\mathbf{x})=\sqrt{(x_{tr}-o_x)^2+(y_{tr}-o_y)^2}-(o_r+R+R_s)\]RTC-CBF

\[h_{tl}(\mathbf{x})=\sqrt{(x_{tl}-o_x)^2+(y_{tl}-o_y)^2}-(o_r+R+R_s)\]LTC-CBF

\(h_{tr}\ge 0\): the right turning circle is clear, so the ship can always escape by turning right
\(h_{tl}\ge 0\): the left turning circle is clear, so the ship can always escape by turning left

Now, here is our simple geometric idea. We call it the turning circle-based CBF, or TC-CBF.

Imagine a ship moving forward. If it turns as hard as it can, to the left or to the right, it follows a circle on that side. We call these the left and right turning circles.

Please look at the figure. The radius R depends on the current speed and the maximum turning rate. R equals alpha times the speed u, divided by r max. alpha is a scaling factor. A larger alpha makes the circle bigger and the turn smoother.

Now, the safety idea is very simple. We just keep the turning circle away from the obstacle. As shown in the figure, we measure the distance from the center of the turning circle to the obstacle. This distance should be larger than R plus the safety radius.

From this, we define two CBFs: one for the right turning circle, called the RTC-CBF, and one for the left turning circle, called the LTC-CBF. If the right turning circle is clear, the ship has a safe way to escape by turning right. If the left circle is clear, it can escape by turning left.

Proposed method · Visualization of TC-CBF constraints

RTC or LTC-CBF: choose the avoidance side

Nominal control input Safe control input (filtered by TC-CBF-QP)

RTC-CBF

Right-side avoidance

The filtered input turns the vehicle to starboard, keeping the right turning circle clear

LTC-CBF

Left-side avoidance

The filtered input turns the vehicle to port, keeping the left turning circle clear

By choosing the RTC-CBF or the LTC-CBF, we can explicitly choose the avoidance direction

Proposed method · Overall framework

COLREGs choose the side, TC-CBF keeps it safe

LOS guidance
+ PD control

Waypoint path

Safety filter · TC-CBF-QP

\[\begin{aligned}\mathbf{u}^{*}=\;&\arg\min_{\mathbf{u}\in\mathbb{R}^m}\ \|\mathbf{u}-\mathbf{u}_n\|_Q^2\\ \text{s.t.}\;\;&\dot h_{i,\sigma_i}(\mathbf{x})+\gamma_i\,h_{i,\sigma_i}(\mathbf{x})\ge 0,\quad i=1,\dots,n\\ &\mathbf{u}_{\min}\le\mathbf{u}\le\mathbf{u}_{\max}\end{aligned}\]

ASVown ship

Decision makingCOLREGs rules

Traffic ship \(i\)\(i=1,\dots,n\)

\(\mathbf{u}_n\) \(\mathbf{u}\) \(\mathbf{r}\) \(\mathbf{x}\) \(\sigma_i\in\{\mathrm{L},\mathrm{R}\}\): LTC- or RTC-CBF chosen for each traffic ship

Decision-making module

COLREGs encounter classification

Encounter geometry: own ship heading psi_o and speed V_o, traffic ship heading psi_t and speed V_t, and the bearing beta_ot from the own ship to the traffic ship

Encounter classification maps for the own ship and the traffic ship over relative heading psi_OT and bearing beta_OT

Head-on Starboard crossing Overtaking Port crossing Overtaken

Classifies each traffic ship by bearing \(\beta_{OT}\) and relative heading \(\psi_{OT}\), then applies only the constraint for the side the rule requires

e.g., head-on → alter course to starboard → RTC-CBF

Results · One-to-one encounter simulations

Tuning \(\alpha\) and \(\gamma\): when and how wide to avoid

Turning-circle scale \(\alpha\)fixed \(\gamma=0.02\)

Own ship trajectories in a starboard-crossing encounter for alpha = 1, 2, 3, 5 and 10 with gamma = 0.02: larger alpha starts the avoidance earlier with a smoother path

CBF parameter \(\gamma\)fixed \(\alpha=5\)

Own ship trajectories for gamma = 0.005, 0.007, 0.01, 0.02 and 0.03 with alpha = 5: smaller gamma gives a wider avoidance

Scenario

Starboard-crossing encounter

The traffic ship (red) crosses from the starboard side; the own ship gives way by turning to starboard and passing astern. Snapshots every 150 s.

\(\alpha\uparrow\)

Larger turning circle → earlier and smoother avoidance

\(\gamma\downarrow\)

More conservative constraint → larger avoidance distance

Results · Multi-ship encounter simulation · own ship + 6 traffic ships

Comparable to MPC, 167× faster on average

Proposed (TC-CBF-QP) Proposed method: the own ship (red) follows the straight path along y = 0 and avoids six traffic ships; snapshots at t = 1000, 2000, 3000 and 4000 s

Proposed method: the own ship (red) follows the straight path along y = 0 and avoids six traffic ships; snapshots at t = 1000, 2000, 3000 and 4000 s

MPC-based

167×

faster on average
23.35 → 0.14 ms

−29%

control effort
8.66 → 6.16

Controller	Avg. comp. time*	Max. comp. time	Avg. CTE	Max. CTE	Control effort**
Proposed (TC-CBF-QP)	0.14 ms	1.80 ms	439.5 m	992.4 m	6.16
MPC-based	23.35 ms	40.18 ms	390.6 m	1001.2 m	8.66

Bold: better · CTE: cross-track error from the reference path · both methods avoid all traffic ships and return to the path

Results · Multi-ship encounter simulation · four ships crossing at the center

Four ships at once: 140× faster than MPC

Proposed

MPC-based

Proposed · animation

140×

faster on average
12.60 → 0.09 ms

−20%

control effort
15.29 → 12.25

Controller	Avg. comp. time*	Max. comp. time	Avg. CTE	Max. CTE	Control effort**
Proposed (TC-CBF-QP)	0.09 ms	1.62 ms	61.4 m	228.6 m	12.25
MPC-based	12.60 ms	38.70 ms	52.9 m	164.9 m	15.29

Bold: better · MPC tracks the path slightly better (lower CTE), while the proposed method needs less control effort

Results · Complex traffic simulations

Computation stays about 0.1 ms as traffic grows

8 ASVs

10 ASVs

Computation time vs. number of ships

Ships	Avg. comp. time*	Max. comp. time
6	0.111 ms	1.934 ms
8	0.117 ms	1.947 ms
10	0.128 ms	1.962 ms

The average time increases only slightly and linearly with the number of ships
The maximum stays below 2 ms in every case

Conclusion

Rule-compliant, direction-aware, and lightweight

🧭 TC-CBF-based COLREGs-compliant safety filter

Developed a TC-CBF-QP-based framework ensuring rule-compliant and direction-aware collision avoidance
Incorporated ship turning capability through left/right CBFs (LTC-CBF, RTC-CBF)

⚡ Efficient and high-performance

Achieved MPC-level avoidance performance with significantly lower computational cost across diverse encounter scenarios
Computation time grows only slightly with traffic: below 2 ms even with 10 ships

0.09–0.14ms

average computation time in the multi-ship encounters

140–167×

faster than MPC on average

< 2ms

maximum computation time, with up to 10 ships

Thank you

Questions & discussion

✉️ leeck@kongju.ac.kr Changyu Lee · Kongju National University

Additional papers applying TC-CBF

MPC-TCCBF avoids a static obstacle with a smaller detour and without slowing down, compared with distance-based CBFs under six parameter settings

IEEE TCST · 2026DOI arXiv

Turning Circle-based Control Barrier Function for Efficient Collision Avoidance of Nonholonomic Vehicles

Changyu Lee, Kiyong Park, Jinwhan Kim*

Multimodal trajectory planning with 16 candidate avoidance modes along a 33.7 km route in dense traffic

Under review

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

Changyu Lee*

This talkChangyu Lee, Jinwook Park, Jinwhan Kim*, “Efficient COLREGs-Compliant Collision Avoidance using Turning Circle-based Control Barrier Function,” Mechatronics, 2026 · DOI · arXiv