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Residual Descent Differential Dynamic Game (RD3G) -- A Fast Newton Solver for Constrained General Sum Games

Zhiyuan Zhang, Panagiotis Tsiotras

TL;DR

The proposed RD3G solver seeks a local Nash equilibrium for games where agents are coupled through their rewards and state constraints by maintaining a dynamic set of active constraints, combined with a barrier function on satisfied constraints and a backtracking line search.

Abstract

We present Residual Descent Differential Dynamic Game (RD3G), a Newton-based solver for constrained multi-agent game-control problems. The proposed solver seeks a local Nash equilibrium for problems where agents are coupled through their rewards and state constraints. We compare the proposed method against competing state-of-the-art techniques and showcase the computational benefits of the RD3G algorithm on several example problems.

Residual Descent Differential Dynamic Game (RD3G) -- A Fast Newton Solver for Constrained General Sum Games

TL;DR

The proposed RD3G solver seeks a local Nash equilibrium for games where agents are coupled through their rewards and state constraints by maintaining a dynamic set of active constraints, combined with a barrier function on satisfied constraints and a backtracking line search.

Abstract

We present Residual Descent Differential Dynamic Game (RD3G), a Newton-based solver for constrained multi-agent game-control problems. The proposed solver seeks a local Nash equilibrium for problems where agents are coupled through their rewards and state constraints. We compare the proposed method against competing state-of-the-art techniques and showcase the computational benefits of the RD3G algorithm on several example problems.
Paper Structure (16 sections, 10 equations, 4 figures, 2 tables, 2 algorithms)

This paper contains 16 sections, 10 equations, 4 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contributions
  4. Problem Formulation
  5. Solution Approach
  6. Constraint Partition
  7. Residual Descent
  8. Backtracking Line Search
  9. Experiments
  10. Implementation
  11. Numerical Examples
  12. Car Merging
  13. Car Racing
  14. Physical Experiments
  15. Discussion
  16. ...and 1 more sections

Figures (4)

  • Figure 1: Merging example with three cars, (a)-(c): Snapshots during merge, (d) Trajectory plot.
  • Figure 2: Merging example with 5 and 8 cars.
  • Figure 3: BuzzRacer system components.
  • Figure 4: Video screenshots of an overtake during the experiment.