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Distributed Differentiable Dynamic Game for Multi-robot Coordination

Yizhi Zhou, Wanxin Jin, Xuan Wang

TL;DR

The D3G framework is developed, which can efficiently solve the forward and inverse problems in multi-robot coordination and proposes a differentiation solver based on Differential Pontryagin's Maximum Principle, which allows each robot to update its parameters in a distributed and coordinated manner.

Abstract

This paper develops a Distributed Differentiable Dynamic Game (D3G) framework, which can efficiently solve the forward and inverse problems in multi-robot coordination. We formulate multi-robot coordination as a dynamic game, where the behavior of a robot is dictated by its own dynamics and objective that also depends on others' behavior. In the forward problem, D3G enables all robots collaboratively to seek the Nash equilibrium of the game in a distributed manner, by developing a distributed shooting-based Nash solver. In the inverse problem, where each robot aims to find (learn) its objective (and dynamics) parameters to mimic given coordination demonstrations, D3G proposes a differentiation solver based on Differential Pontryagin's Maximum Principle, which allows each robot to update its parameters in a distributed and coordinated manner. We test the D3G in simulation with two types of robots given different task configurations. The results demonstrate the effectiveness of D3G for solving both forward and inverse problems in comparison with existing methods.

Distributed Differentiable Dynamic Game for Multi-robot Coordination

TL;DR

The D3G framework is developed, which can efficiently solve the forward and inverse problems in multi-robot coordination and proposes a differentiation solver based on Differential Pontryagin's Maximum Principle, which allows each robot to update its parameters in a distributed and coordinated manner.

Abstract

This paper develops a Distributed Differentiable Dynamic Game (D3G) framework, which can efficiently solve the forward and inverse problems in multi-robot coordination. We formulate multi-robot coordination as a dynamic game, where the behavior of a robot is dictated by its own dynamics and objective that also depends on others' behavior. In the forward problem, D3G enables all robots collaboratively to seek the Nash equilibrium of the game in a distributed manner, by developing a distributed shooting-based Nash solver. In the inverse problem, where each robot aims to find (learn) its objective (and dynamics) parameters to mimic given coordination demonstrations, D3G proposes a differentiation solver based on Differential Pontryagin's Maximum Principle, which allows each robot to update its parameters in a distributed and coordinated manner. We test the D3G in simulation with two types of robots given different task configurations. The results demonstrate the effectiveness of D3G for solving both forward and inverse problems in comparison with existing methods.
Paper Structure (11 sections, 1 theorem, 19 equations, 8 figures)

This paper contains 11 sections, 1 theorem, 19 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Formulation
  3. Parametric Dynamic Game for Multi-robot Coordination
  4. Problem Formulation
  5. Inverse Learning for Distributed Differential Dynamic Game
  6. Method Overview
  7. A Fully Distributed Solver for Diff-KKT
  8. Experiments
  9. Conclusion and Future Work
  10. Forward Problem: Distributed Nash Seeking
  11. Proof of Lemma \ref{['LM_alg3']}

Key Result

Lemma III.1

(Validity of Algorithm Algorithm_DPMPsolver): Suppose the network $\mathbb{G}$ is undetected and connected, suppose equation set eq_GLE has a unique solution, by Algorithm Algorithm_DPMPsolver, if the positive step-size $\delta$ is sufficiently small, the state $\bm{Y}_i^{\tau}$ of robot $i$ will co

Figures (8)

  • Figure 1: Each robot possesses a local optimal control $\mathbf{P}_i$, which together constitutes a dynamic game. The Nash equilibrium of the game reconstructs robot coordination. Problem of interest: Distributed inverse learning (blue) of parameterized objective functions from demonstration for robot coordination. The learned objective is generalizable (red) to new environments.
  • Figure 2: Experimental Platform: Turtlebot3 and its model.
  • Figure 3: Gazebo environment for scenarios c) and d).
  • Figure 4: Learning fixed swapping tasks with sixteen robots.
  • Figure 5: Comparison of computation time with GT-IRL and IKKT.
  • ...and 3 more figures

Theorems & Definitions (1)

  • Lemma III.1