# Distributed Differentiable Dynamic Game for Multi-robot Coordination

arXiv: https://arxiv.org/abs/2207.08892 · HTML: https://mlsanity.com/paper/2207.08892/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 48 references that are in the map.
- First posted on arXiv 18 Jul 2022.

## Builds on (most cited first, 13 of 13)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms](https://mlsanity.com/paper/1911.10635/) (2019)
- [A Survey and Critique of Multiagent Deep Reinforcement Learning](https://mlsanity.com/paper/1810.05587/) (2018)
- [Pontryagin Differentiable Programming: An End-to-End Learning and Control Framework](https://mlsanity.com/paper/1912.12970/) (2019)
- [Efficient Iterative Linear-Quadratic Approximations for Nonlinear Multi-Player General-Sum Differential Games](https://mlsanity.com/paper/1909.04694/) (2019)
- [Safe Pontryagin Differentiable Programming](https://mlsanity.com/paper/2105.14937/) (2021)
- [Saddle-point dynamics: conditions for asymptotic stability of saddle points](https://mlsanity.com/paper/1510.02145/) (2015)
- [LUCIDGames: Online Unscented Inverse Dynamic Games for Adaptive Trajectory Prediction and Planning](https://mlsanity.com/paper/2011.08152/) (2020)
- [Inferring Objectives in Continuous Dynamic Games from Noise-Corrupted Partial State Observations](https://mlsanity.com/paper/2106.03611/) (2021)
- [Learning from Sparse Demonstrations](https://mlsanity.com/paper/2008.02159/) (2020)
- [Distributed Nash Equilibrium Seeking by A Consensus Based Approach](https://mlsanity.com/paper/1602.00771/) (2016)
- [Consensus-based Distributed Optimization Enhanced by Integral Feedback](https://mlsanity.com/paper/2111.09346/) (2021)
- [Geometric Convergence of Distributed Gradient Play in Games with Unconstrained Action Sets](https://mlsanity.com/paper/1907.07144/) (2019)

## Built on by (most cited first, 1 of 1)

- [State-of-the-art in Robot Learning for Multi-Robot Collaboration: A Comprehensive Survey](https://mlsanity.com/paper/2408.11822/) (2024)

## Abstract (arXiv)

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.