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Optimal Integrated Task and Path Planning and Its Application to Multi-Robot Pickup and Delivery

Aman Aryan, Manan Modi, Indranil Saha, Rupak Majumdar, Swarup Mohalik

TL;DR

This work tackles multi-robot pickup-and-delivery in static warehouse environments by proposing an integrated planning framework that tightly couples an SMT-based task planner with an optimal path planner (CBS-PC). The approach iteratively refines task assignments and collision-free trajectories, with formal optimality guarantees and a proof of completeness. Empirical results show the integrated planner achieves faster computation and higher-quality plans than state-of-the-art classical planners like ENHSP, especially when collaboration via intermediate locations is allowed. The framework supports practical constraints such as deadlines and payload capacities, offering scalable, collision-free MAPD solutions with real-world relevance for warehouse automation.

Abstract

We propose a generic multi-robot planning mechanism that combines an optimal task planner and an optimal path planner to provide a scalable solution for complex multi-robot planning problems. The Integrated planner, through the interaction of the task planner and the path planner, produces optimal collision-free trajectories for the robots. We illustrate our general algorithm on an object pick-and-drop planning problem in a warehouse scenario where a group of robots is entrusted with moving objects from one location to another in the workspace. We solve the task planning problem by reducing it into an SMT-solving problem and employing the highly advanced SMT solver Z3 to solve it. To generate collision-free movement of the robots, we extend the state-of-the-art algorithm Conflict Based Search with Precedence Constraints with several domain-specific constraints. We evaluate our integrated task and path planner extensively on various instances of the object pick-and-drop planning problem and compare its performance with a state-of-the-art multi-robot classical planner. Experimental results demonstrate that our planning mechanism can deal with complex planning problems and outperforms a state-of-the-art classical planner both in terms of computation time and the quality of the generated plan.

Optimal Integrated Task and Path Planning and Its Application to Multi-Robot Pickup and Delivery

TL;DR

This work tackles multi-robot pickup-and-delivery in static warehouse environments by proposing an integrated planning framework that tightly couples an SMT-based task planner with an optimal path planner (CBS-PC). The approach iteratively refines task assignments and collision-free trajectories, with formal optimality guarantees and a proof of completeness. Empirical results show the integrated planner achieves faster computation and higher-quality plans than state-of-the-art classical planners like ENHSP, especially when collaboration via intermediate locations is allowed. The framework supports practical constraints such as deadlines and payload capacities, offering scalable, collision-free MAPD solutions with real-world relevance for warehouse automation.

Abstract

We propose a generic multi-robot planning mechanism that combines an optimal task planner and an optimal path planner to provide a scalable solution for complex multi-robot planning problems. The Integrated planner, through the interaction of the task planner and the path planner, produces optimal collision-free trajectories for the robots. We illustrate our general algorithm on an object pick-and-drop planning problem in a warehouse scenario where a group of robots is entrusted with moving objects from one location to another in the workspace. We solve the task planning problem by reducing it into an SMT-solving problem and employing the highly advanced SMT solver Z3 to solve it. To generate collision-free movement of the robots, we extend the state-of-the-art algorithm Conflict Based Search with Precedence Constraints with several domain-specific constraints. We evaluate our integrated task and path planner extensively on various instances of the object pick-and-drop planning problem and compare its performance with a state-of-the-art multi-robot classical planner. Experimental results demonstrate that our planning mechanism can deal with complex planning problems and outperforms a state-of-the-art classical planner both in terms of computation time and the quality of the generated plan.
Paper Structure (31 sections, 1 theorem, 17 equations, 18 figures, 2 algorithms)

This paper contains 31 sections, 1 theorem, 17 equations, 18 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem
  3. Preliminaries
  4. Workspace
  5. Robots
  6. Tasks
  7. Plan and Trajectory
  8. Optimality Criteria for a Trajectory
  9. Problem Definition
  10. Integrated Task and Path Planning Algorithm
  11. Applications to Warehouse Management
  12. Task Planning Algorithm
  13. SMT Encodings Of Constraints
  14. Completing pick-and-drop tasks
  15. Enabling collaboration
  16. ...and 16 more sections

Key Result

Theorem 1

There does not exist a task assignment for which the cost of the collision-free trajectories would be less than the cost of the trajectories returned by Algorithm alg:Algorithm1.

Figures (18)

  • Figure 1: Examples of workspaces showing warehouse scenarios a) without Intermediate Location, b) with an Intermediate Location.
  • Figure 2: Trajectories of the two robots for the problem shown in Figure \ref{['fig:example']}(a)
  • Figure 3: Trajectories of the two robots for the problem shown in Figure \ref{['fig:example']}(b)
  • Figure 4: Predefined (left) and Randomly generated (right) 50x50 map
  • Figure 5: Task Planner : The effect of increasing the number of robots (shown in legends) and the number of tasks for task planner with makespan optimization criteria on a) Computation Time (left) and b) Makespan (right)
  • ...and 13 more figures

Theorems & Definitions (7)

  • Definition 1: Plan
  • Definition 2: Trajectory
  • Definition 3: Makespan
  • Definition 4: Total cost
  • Definition 5: Problem
  • Theorem 1: Optimality
  • proof