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Multi-Robot Trajectory Generation via Consensus ADMM: Convex vs. Non-Convex

Jushan Chen

TL;DR

The paper investigates how Consensus ADMM (C-ADMM) performs for multi-robot trajectory planning under convex versus non-convex collision constraints. It proposes a convex variant using Buffered Voronoi Cells (BVCs) to replace non-convex collision constraints, and a non-convex baseline with standard pairwise collision avoidance, both cast in a receding-horizon distributed MPC framework. Through simulated multi-robot waypoint transitions and Monte Carlo analyses, the study shows that the convex C-ADMM with BVCs converges substantially faster (e.g., about 1000 fewer iterations in a 5-robot scenario) and yields safer trajectories, while the non-convex baseline can violate safety constraints and produce sub-optimal solutions. The findings highlight the trade-offs between distributed optimization convergence and collision-avoidance formulations, informing design choices for scalable, safe multi-robot coordination in practical applications.

Abstract

C-ADMM is a well-known distributed optimization framework due to its guaranteed convergence in convex optimization problems. Recently, C-ADMM has been studied in robotics applications such as multi-vehicle target tracking and collaborative manipulation tasks. However, few works have investigated the performance of C-ADMM applied to non-convex problems in robotics applications due to a lack of theoretical guarantees. For this project, we aim to quantitatively explore and examine the convergence behavior of non-convex C-ADMM through the scope of distributed multi-robot trajectory planning. We propose a convex trajectory planning problem by leveraging C-ADMM and Buffered Voronoi Cells (BVCs) to get around the non-convex collision avoidance constraint and compare this convex C-ADMM algorithm to a non-convex C-ADMM baseline with non-convex collision avoidance constraints. We show that the convex C-ADMM algorithm requires 1000 fewer iterations to achieve convergence in a multi-robot waypoint navigation scenario. We also confirm that the non-convex C-ADMM baseline leads to sub-optimal solutions and violation of safety constraints in trajectory generation.

Multi-Robot Trajectory Generation via Consensus ADMM: Convex vs. Non-Convex

TL;DR

The paper investigates how Consensus ADMM (C-ADMM) performs for multi-robot trajectory planning under convex versus non-convex collision constraints. It proposes a convex variant using Buffered Voronoi Cells (BVCs) to replace non-convex collision constraints, and a non-convex baseline with standard pairwise collision avoidance, both cast in a receding-horizon distributed MPC framework. Through simulated multi-robot waypoint transitions and Monte Carlo analyses, the study shows that the convex C-ADMM with BVCs converges substantially faster (e.g., about 1000 fewer iterations in a 5-robot scenario) and yields safer trajectories, while the non-convex baseline can violate safety constraints and produce sub-optimal solutions. The findings highlight the trade-offs between distributed optimization convergence and collision-avoidance formulations, informing design choices for scalable, safe multi-robot coordination in practical applications.

Abstract

C-ADMM is a well-known distributed optimization framework due to its guaranteed convergence in convex optimization problems. Recently, C-ADMM has been studied in robotics applications such as multi-vehicle target tracking and collaborative manipulation tasks. However, few works have investigated the performance of C-ADMM applied to non-convex problems in robotics applications due to a lack of theoretical guarantees. For this project, we aim to quantitatively explore and examine the convergence behavior of non-convex C-ADMM through the scope of distributed multi-robot trajectory planning. We propose a convex trajectory planning problem by leveraging C-ADMM and Buffered Voronoi Cells (BVCs) to get around the non-convex collision avoidance constraint and compare this convex C-ADMM algorithm to a non-convex C-ADMM baseline with non-convex collision avoidance constraints. We show that the convex C-ADMM algorithm requires 1000 fewer iterations to achieve convergence in a multi-robot waypoint navigation scenario. We also confirm that the non-convex C-ADMM baseline leads to sub-optimal solutions and violation of safety constraints in trajectory generation.
Paper Structure (12 sections, 9 equations, 3 figures, 2 tables, 1 algorithm)

This paper contains 12 sections, 9 equations, 3 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction & Motivation
  2. Problem Formulation
  3. Multi-robot Trajectory Optimization
  4. Variant 1: Convex Trajectory Optimization via C-ADMM with BVCs
  5. Variant 2: Non-convex trajectory optimization via C-ADMM
  6. C-ADMM in receding horizon control
  7. Challenges
  8. Simulation studies
  9. Multi-agent waypoint transition
  10. Convergence Analysis
  11. Monte Carlo Anlysis
  12. Conclusion

Figures (3)

  • Figure 1: Trajectory comparison of our convex C-ADMM and the non-convex C-ADMM baseline on a 5-drone navigation scenario. From left to right, we show the side view of the trajectory and the bird's eye view of the trajectory.
  • Figure 2: Pairwise distances between all robots in the 5-robot waypoint navigation scenario
  • Figure 3: From top to bottom, we show the global objective descent and primal residual descent for both our convex C-ADMM method and the non-convex baseline