Dubins Path
Dubins Shortest Path Problem · Also known as: Dubins curve, RSR path, LSL path
The Dubins path is the shortest curve connecting two points in the plane with prescribed initial and terminal tangent directions, subject to a constraint on curvature. Introduced by Lester Dubins in 1957, it solved a fundamental problem in differential geometry and became essential in motion planning for aircraft, helicopters, and autonomous vehicles. A Dubins path consists of circular arcs and straight line segments arranged in a sequence such as RSR (Right-Straight-Right) or LSL (Left-Straight-Left).
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When to use it
Use Dubins paths when planning trajectories for vehicles with limited turning radius and fixed speed. Ideal for fixed-wing aircraft, differential-drive robots, and nonholonomic systems. Dubins paths are computationally efficient and exact, making them suitable for real-time planning. Prefer this method when the environment is obstacle-free or when combined with obstacle avoidance (Dubins + RRT). Use when you need optimality guarantees; for more complex environments, combine with sampling-based methods.
Strengths & limitations
- Mathematically optimal for the unconstrained problem; guaranteed shortest path given the constraints.
- Closed-form solution; no iterative optimization needed; very fast computation.
- Elegant and simple; six candidate paths reduce the search space to a tractable problem.
- Well-studied in the literature; multiple implementations and extensions available.
- No obstacle avoidance; assumes a clear workspace. Extension with RRT or PRM needed for cluttered environments.
- Assumes constant speed and fixed turning radius; does not handle variable dynamics or acceleration constraints.
- Limited to 2D (planar) problems; extension to 3D (with pitch constraints) requires modifications.
- Assumes known initial and terminal headings; if these are not specified, an outer optimization loop is needed.
Frequently asked
What are the six Dubins path configurations?
The six configurations are: Left-Straight-Left (LSL), Right-Straight-Right (RSR), Left-Right-Left (LRL), Right-Left-Right (RLR), Left-Straight-Right (LSR), and Right-Straight-Left (RSL). The first three are CCC (three-circle) types, and the last three are CSC (circle-straight-circle) types. Not all are always feasible for a given problem; at least one is always optimal.
How do I compute the length of a Dubins path?
After normalizing coordinates and solving the geometric configuration, compute the arc lengths and straight-segment length. For a CSC path: L = r(alpha + beta) + d, where alpha and beta are arc angles (radians), r is the turning radius, and d is the straight segment length. For CCC paths, use analogous formulas.
Can Dubins paths handle obstacles?
Pure Dubins paths assume an obstacle-free environment. To navigate around obstacles, combine Dubins paths with sampling-based planners (RRT, PRM) or use Dubins paths for local waypoint connection between safe regions. Some methods compute Dubins paths on visibility graphs.
What is the minimum turning radius and how does it affect the path?
The minimum turning radius r is a property of the vehicle (e.g., a fixed-wing aircraft has r = v^2 / (g * tan(phi_max)). Larger r forces wider, longer paths. Smaller r allows tighter, shorter paths. The radius directly scales the path length and must be respected by the vehicle's dynamics.
Sources
- Dubins, L. E. (1957). On curves of minimal length with a constraint on average curvature and with prescribed initial and terminal positions and tangents. American Journal of Mathematics, 79(3), 497–516. DOI: 10.2307/2372560 ↗
- Shkel, A. M., & Lumelsky, V. (2001). Classification of the Dubins set. Robotics and Autonomous Systems, 34(2-3), 179–202. DOI: 10.1016/s0921-8890(00)00127-5 ↗
- Hota, S., & Ghose, D. (2016). Optimal path planning for aerial vehicles using Dubins curves. IEEE Transactions on Aerospace and Electronic Systems, 52(3), 1400–1416. link ↗
How to cite this page
ScholarGate. (2026, June 3). Dubins Shortest Path Problem. ScholarGate. https://scholargate.app/en/aerospace/dubins-path
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