Dubins Car

• Also called: Dubins vehicle
• Category: Planning & manipulation › Motion planning
• Tags: motion-planning, kinematics, nonholonomic, fixed-wing, path-planning

A planar vehicle model that moves forward at constant speed with a bounded turning rate; its shortest paths between two poses consist of at most three arcs and straight segments.

Definition

The Dubins car is a kinematic model of a vehicle that can only move forward at a fixed speed and cannot turn tighter than a minimum radius. Its state is position (x, y) and heading θ, and its motion follows ẋ = v cos θ, ẏ = v sin θ, θ̇ = u with |u| ≤ v / R_min. Compared with the unicycle model, which allows any forward speed as well as stopping, reversing and turning in place, the Dubins car has constant speed and bounded curvature, so it can neither stop nor turn on the spot. Like the unicycle, it is subject to a nonholonomic constraint: it cannot move sideways.

The model is named after Lester Dubins, who proved in 1957 that the shortest path of bounded curvature between two poses in the obstacle-free plane consists of at most three segments, each either a straight line (S) or a minimum-radius circular arc turning left (L) or right (R). Only six combinations can be optimal: LSL, RSR, LSR, RSL, LRL and RLR, so a planner can compute every candidate in closed form and keep the shortest. Reeds and Shepp (1990) extended the result to a car that can also reverse, giving the Reeds-Shepp car with a larger family of optimal paths.

Dubins paths are a standard building block for planning fixed-wing aircraft, boats and car-like robots. Sampling-based planners such as RRT and RRT* use them as a local steering function, and coverage and routing planners use them to order waypoints under curvature limits. Three-dimensional extensions, often called the Dubins airplane, add altitude with a bounded climb or descent rate. The model has limits worth remembering: real vehicles cannot switch instantly between full-left, straight and full-right turning, so curvature jumps at segment joins must be smoothed by the controller or by planning with clothoids or other continuous-curvature paths, and wind or currents change ground speed in ways the pure model ignores.

Why it matters

Many vehicles, including fixed-wing drones, boats and cars at speed, really are limited to forward motion and a minimum turn radius. The Dubins car captures that in the simplest possible model and gives closed-form shortest paths, which makes it a reference point for planning and control of such vehicles.

Key applications

• Path planning for fixed-wing UAVs
• Steering functions in sampling-based planners for car-like robots
• Waypoint routing for marine vehicles
• Curvature-constrained coverage and inspection paths
• Routing problems with turning limits, such as the Dubins traveling salesman problem

In practice

A fixed-wing survey drone must pass through a list of waypoints, each with a required heading. The planner computes the Dubins path between consecutive waypoint poses using the aircraft's minimum turn radius at cruise speed, with a margin for wind, and chains the results into a route that a guidance law then follows segment by segment. When several such aircraft must coordinate, as in distributed path-following work that models fixed-wing aircraft as 3D Dubins vehicles, the coordination law has to work without the option of slowing to a stop or waiting in place.

Common misconceptions

• The Dubins car and the unicycle model are the same — the unicycle can vary speed, stop and turn in place, while the Dubins car moves forward at constant speed with bounded curvature
• Dubins paths can be followed exactly by real vehicles — they contain instantaneous changes in curvature that real steering or banking must smooth
• Dubins solutions are optimal among obstacles — the six-path result holds in the obstacle-free plane; with obstacles, Dubins segments are only local connections inside a broader planner

Who should know this

• Fixed-wing UAV guidance and planning engineers
• Motion planning researchers
• Marine and autonomous vehicle developers
• Robotics students learning nonholonomic planning

Related technologies

• Reeds-Shepp Curves
• Dubins Airplane Model
• Clothoid Paths
• Open Motion Planning Library (OMPL)
• Hybrid A*

Related terms

• Unicycle Model
• Nonholonomic Constraint
• RRT*
• Trajectory Planning
• UAV
• Formation Control

Related projects

• ArduPilot: World's most trusted open-source autopilot for drones, planes, rovers, and submarines
• Nav2: ROS 2 navigation stack with path planning and obstacle avoidance for mobile robots
• ROS Motion Planning: One repo implementing 40+ classic and learning-based robot path planners as ROS plugins
• OMPL: Sampling-based motion planning library powering MoveIt and countless robotics applications
• MoveIt 2: Motion planning framework for ROS 2 robot arms, with kinematics and collision checking
• PyRoki: Modular Python toolkit for kinematic optimization across CPU, GPU, and TPU via JAX