Robot Path Planning: RRT Algorithm and Worked Example

Introduction

Robot path planning determines how a mechanism moves from its starting configuration to a goal without colliding with its surroundings. This guide explains configuration space, the RRT algorithm, and the difference between a geometric path and an executable trajectory. These ideas connect undergraduate robotics, machine kinematics, and industrial offline programming.

Robot Path Planning in Configuration Space

A robot configuration describes all independent coordinates needed to specify its position, such as the joint angles of a six-axis manipulator. Engineers collect these coordinates into a vector, q = [q1, q2, …, qn], so one point in configuration space represents the entire robot rather than only its tool tip.

An obstacle occupies every configuration in which any robot component intersects it. Consequently, a clear straight line between two tool positions does not guarantee a collision-free movement: the elbow, wrist, gripper, or carried workpiece may strike a fixture.

A geometric path is a continuous sequence q(s), with 0 ≤ s ≤ 1, linking valid start and goal configurations. Inverse kinematics supplies candidate joint configurations for a desired tool pose, but motion planning must still connect those candidates through collision-free space. Northwestern University’s Modern Robotics resource explains this configuration-space interpretation.

Robot Path Planning with the RRT Algorithm

A rapidly-exploring random tree, or RRT, builds a search tree outward from the starting configuration. Each iteration samples a configuration, finds the nearest existing node, and attempts a short extension toward the sample. The planner adds that extension only after checking its motion for collisions.

For a simple Euclidean configuration space, the extension rule is qnew = qnear + α(qsample − qnear), where α = min(1, δ/d), d = ||qsample − qnear||, and δ is the maximum step length. Revolute joints require appropriate angle wrapping, and mixed angular and linear coordinates require a carefully chosen distance metric.

As an illustrative calculation, consider a translating point robot at (0, 0) m, a sample at (3, 4) m, and δ = 0.20 m. The distance is 5 m, so α = 0.04 and the proposed new node is (0.12, 0.16) m. Accept it only if the entire connecting segment is clear, not merely its endpoints.

Occasionally sampling the goal encourages connection to the destination. Basic RRT prioritises finding a feasible route rather than guaranteeing the shortest route; RRT-star adds rewiring to improve solution quality under its theoretical assumptions. Modern Robotics’ sampling-methods lesson details these distinctions.

Robotic Welding: A Current Research Application

Welding cells require different motions for depositing metal, approaching a joint, retreating from it, and travelling between seams. A single shortest-path objective may ignore torch orientation, fixture clearance, or the practical requirements of those different operations.

A 2026 Discover Mechanical Engineering study by Hong, Chu, and Wang, published on 6 October, separates these welding motions into distinct path types. It combines local torch-attitude adjustments with global planning using Adaptive Batch Informed Trees, or ABIT-star. This is a different planner from RRT, illustrating how the application determines algorithm choice.

The study reports shorter average paths and greater minimum clearance in its tested scenarios, but its improved objective also reduced single-attempt planning success compared with the baseline. That trade-off matters academically: assess planning time, success rate, clearance, and path quality together rather than treating one favourable metric as universal superiority.

Collision Avoidance Mistakes and Exam Tips

Do not confuse path planning with trajectory planning. A trajectory assigns time to the path, producing joint velocities and accelerations that must respect actuator, payload, and process limits. A collision-free geometric route can still demand excessive torque or impractical cycle time.

Check the complete robot geometry, self-collisions, joint limits, and clearance between sampled nodes. Coarse collision checking can miss thin obstacles, while uncertain fixture positions require justified clearance margins. In an exam answer, state the robot model, obstacle assumptions, distance metric, and validation method before comparing algorithms.

Featured photograph: FANUC welding robots by Phasmatisnox, CC BY 3.0; resized for publication.

Conclusion

Robot path planning connects configuration-space geometry, collision detection, and search algorithms to practical machine motion. Distinguish feasible paths from dynamically executable trajectories, evaluate competing performance measures, and explore more mechanical engineering topics on Mechtics.