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Nonlinear receding-horizon differential game for drone racing along a three-dimensional path

Kijin Sung, Kenta Hoshino, Akihiko Honda, Takeya Shima, Toshiyuki Ohtsuka

TL;DR

This work tackles competitive drone racing along three-dimensional paths by formulating a nonlinear receding-horizon differential game (NRHDG) that extends nonlinear model predictive control (NMPC) to account for an adversarial opponent. It introduces a projection-point-based path-following model to avoid iterative distance minimization, a real-time potential function enabling dynamic switching between overtaking and obstructing, and a formal performance metric for comparing NRHDG with NMPC. The authors develop augmented-state dynamics to fuse path-following with flight dynamics, derive zero-sum objective functions for NRHDG, and demonstrate through simulations that NRHDG achieves superior overtaking and obstructing performance. The results suggest NRHDG’s practical impact for robust, real-time multi-agent drone racing and potentially broader multi-agent control problems requiring dynamic role-switching and adversarial planning.

Abstract

Drone racing involves high-speed navigation of three-dimensional paths, posing a substantial challenge in control engineering. This study presents a game-theoretic control framework, the nonlinear receding-horizon differential game (NRHDG), designed for competitive drone racing. NRHDG enhances robustness in adversarial settings by predicting and countering an opponent's worst-case behavior in real time. It extends standard nonlinear model predictive control (NMPC), which otherwise assumes a fixed opponent model. First, we develop a novel path-following formulation based on projection point dynamics, eliminating the need for costly distance minimization. Second, we propose a potential function that allows each drone to switch between overtaking and obstructing maneuvers based on real-time race situations. Third, we establish a new performance metric to evaluate NRHDG with NMPC under race scenarios. Simulation results demonstrate that NRHDG outperforms NMPC in terms of both overtaking efficiency and obstructing capabilities.

Nonlinear receding-horizon differential game for drone racing along a three-dimensional path

TL;DR

This work tackles competitive drone racing along three-dimensional paths by formulating a nonlinear receding-horizon differential game (NRHDG) that extends nonlinear model predictive control (NMPC) to account for an adversarial opponent. It introduces a projection-point-based path-following model to avoid iterative distance minimization, a real-time potential function enabling dynamic switching between overtaking and obstructing, and a formal performance metric for comparing NRHDG with NMPC. The authors develop augmented-state dynamics to fuse path-following with flight dynamics, derive zero-sum objective functions for NRHDG, and demonstrate through simulations that NRHDG achieves superior overtaking and obstructing performance. The results suggest NRHDG’s practical impact for robust, real-time multi-agent drone racing and potentially broader multi-agent control problems requiring dynamic role-switching and adversarial planning.

Abstract

Drone racing involves high-speed navigation of three-dimensional paths, posing a substantial challenge in control engineering. This study presents a game-theoretic control framework, the nonlinear receding-horizon differential game (NRHDG), designed for competitive drone racing. NRHDG enhances robustness in adversarial settings by predicting and countering an opponent's worst-case behavior in real time. It extends standard nonlinear model predictive control (NMPC), which otherwise assumes a fixed opponent model. First, we develop a novel path-following formulation based on projection point dynamics, eliminating the need for costly distance minimization. Second, we propose a potential function that allows each drone to switch between overtaking and obstructing maneuvers based on real-time race situations. Third, we establish a new performance metric to evaluate NRHDG with NMPC under race scenarios. Simulation results demonstrate that NRHDG outperforms NMPC in terms of both overtaking efficiency and obstructing capabilities.

Paper Structure

This paper contains 24 sections, 1 theorem, 30 equations, 12 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Modeling
  3. Dynamics of drone
  4. Dynamics of projection point and arc length
  5. Augmented state equation for path following
  6. Control methods
  7. Nonlinear model predictive control
  8. Nonlinear receding-horizon differential game
  9. Design of objective functions for competitive drone racing
  10. Control objectives
  11. NMPC objective function
  12. Path-following term
  13. Overtaking and obstructing term
  14. Overall NMPC cost
  15. NRHDG objective function
  16. ...and 9 more sections

Key Result

theorem 1

Suppose the path $r: \Theta \to \mathbb{R}^3$ is twice differentiable with $dr(\theta)/d\theta \neq 0$ for any $\theta \in \Theta$, and the trajectory $p_d: [0,t_f] \to \mathbb{R}^3$ of the drone is differentiable for any $t \in [0,t_f]$. If $\theta_d(t)$ is a solution of a differential equation with its initial value $\theta_d(0)$ satisfying (eq:proj), and holds for any $t \in [0,t_f]$, then $p

Figures (12)

  • Figure 1: Overview of the inertial frame and body frame.
  • Figure 2: Relationship between drone and path.
  • Figure 3: Prediction of opponent's motion in NMPC
  • Figure 4: Difference of deviations of two drones.
  • Figure 5: Potential function around ego drone.
  • ...and 7 more figures

Theorems & Definitions (5)

  • theorem 1
  • proof
  • remark 1
  • remark 2
  • remark 3