[Paper] Vehicle Painting Robot Path Planning Using Hierarchical Optimization

Source: arXiv - 2601.00271v1

Overview

The paper tackles a bottleneck in automotive factories: manually crafting paint‑paths for multiple robot arms that coat car bodies moving on a conveyor. By casting the problem as a hierarchical optimization—a high‑level vehicle‑routing‑style assignment followed by low‑level trajectory generation—the authors automate a task that traditionally consumes weeks of engineering effort, while still meeting the strict quality and safety constraints of paint application.

Key Contributions

• Hierarchical formulation that separates the combinatorial assignment of surface patches to robots (upper layer) from the continuous trajectory planning for each robot (lower layer).
• Customizable optimization pipeline: different solvers (e.g., meta‑heuristics for the VRP‑like layer, gradient‑based or sampling planners for the trajectory layer) can be plugged in without redesigning the whole system.
• Domain‑specific encoding: variable representations, repair operators, and initialization strategies that respect painting constraints such as overlap limits, nozzle orientation, and spray‑coverage continuity.
• Empirical validation on three production‑grade vehicle models, showing fully automated paths that meet all constraints and achieve paint quality on par with expert‑crafted solutions.

Methodology

1. Problem Decomposition

   • Upper layer (assignment): The car surface is divided into paint‑able patches. The task is to allocate these patches to the available robots while minimizing travel distance and balancing workload—formally analogous to a Vehicle Routing Problem (VRP).
   • Lower layer (trajectory): For each robot, a detailed 3‑D path is generated that respects nozzle angle, spray distance, overlap/under‑lap limits, and collision avoidance with the car and other robots.

2. Optimization Strategy

   • Upper layer: A population‑based meta‑heuristic (e.g., Genetic Algorithm) explores different patch‑to‑robot assignments. Custom repair operators fix infeasible assignments (e.g., patches that would force a robot to exceed its reachable workspace).
   • Lower layer: Given a feasible assignment, a continuous optimizer (e.g., Sequential Quadratic Programming or sampling‑based planner) refines the robot’s waypoints, inserting intermediate “spray‑passes” to satisfy overlap constraints.

3. Iterative Feedback

   • If the lower‑layer planner fails to produce a valid trajectory for a robot, the upper‑layer solution is penalized and re‑searched, creating a loop that converges to a globally feasible plan.

4. Implementation Details

   • Variable encoding captures both discrete (which robot paints which patch) and continuous (exact nozzle pose) decisions.
   • Initialization seeds the upper layer with a heuristic based on geometric proximity, speeding up convergence.

Results & Findings

• Success Rate: The hierarchical approach produced feasible paint paths for all three test vehicles (compact sedan, midsize SUV, full‑size truck) within a few minutes of computation, compared to days of manual engineering.
• Quality Metrics: Measured overlap uniformity, spray angle deviation, and total robot travel distance were within 2‑3 % of the manually engineered baselines.
• Scalability: Adding an extra robot arm (four‑arm configuration) increased computation time linearly, confirming the method’s suitability for larger production lines.
• Robustness: The repair operators successfully corrected 87 % of initially infeasible assignments, reducing the need for costly re‑runs.

Practical Implications

• Reduced Time‑to‑Market: Automating paint‑path design cuts engineering lead‑time from weeks to hours, accelerating model roll‑outs.
• Consistent Quality: Algorithmic generation eliminates human variability, leading to more uniform paint finishes across production batches.
• Flexibility for Customization: When a new vehicle variant is introduced, the same pipeline can re‑optimize paths on‑the‑fly, supporting low‑volume, high‑mix manufacturing.
• Integration with Existing PLCs: The output is a set of robot joint trajectories and timing schedules that can be directly uploaded to standard industrial robot controllers, requiring minimal changes to the production line software stack.
• Cost Savings: Fewer engineering hours and reduced rework due to paint defects translate into measurable savings, especially for high‑volume plants.

Limitations & Future Work

• Model Fidelity: The current planner assumes a static car geometry; dynamic deformations (e.g., due to temperature) are not modeled.
• Solver Generality: While the hierarchical split works well for painting, adapting it to other coating processes (e.g., powder coating) may require new constraint encodings.
• Real‑World Deployment: Experiments were conducted in simulation and a controlled test cell; full‑scale factory trials are needed to assess robustness against sensor noise and unexpected obstacles.
• Future Directions: The authors suggest extending the framework with learning‑based initialization (e.g., using past paint‑paths to seed the upper layer) and incorporating multi‑objective optimization to balance paint quality against robot wear and energy consumption.

Authors

• Yuya Nagai
• Hiromitsu Nakamura
• Narito Shinmachi
• Yuta Higashizono
• Satoshi Ono

Paper Information

• arXiv ID: 2601.00271v1
• Categories: cs.RO, cs.NE
• Published: January 1, 2026
• PDF: Download PDF