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Vector Cost Behavioral Planning for Autonomous Robotic Systems with Contemporary Validation Strategies

Benjamin R. Toaz, Quentin Goss, John Thompson, Seta Boğosyan, Shaunak D. Bopardikar, Mustafa İlhan Akbaş, Metin Gökaşan

TL;DR

The paper addresses robust multi-objective behavioral planning for autonomous robots by modeling decision-making as a vector cost bimatrix game and preserving objective structure under uncertainty. It advances a convex-optimization-based cost adjustment within a potential-game framework to enforce Nash equilibria that align with security policies, and it demonstrates that a radial-basis-like cost redesign improves convergence for higher-dimensional objective sets. The approach is validated through a circular racing scenario, leveraging SHAP for explainability and SEMBAS for boundary-focused sensitivity analysis, showing superior robustness and interpretability compared to scalarized baselines. This integrated V&V pipeline enhances transparency, robustness to weight perturbations, and practical applicability of multi-objective game-theoretic planning in autonomous systems.

Abstract

The vector cost bimatrix game is a method for multi-objective decision making that enables autonomous robotic systems to optimize for multiple goals at once while avoiding worst-case scenarios in neglected objectives. We expand this approach to arbitrary numbers of objectives and compare its performance to scalar weighted sum methods during competitive motion planning. Explainable Artificial Intelligence (XAI) software is used to aid in the analysis of high dimensional decision-making data. State-space Exploration of Multidimensional Boundaries using Adherence Strategies (SEMBAS) is applied to explore performance modes in the parameter space as a sensitivity study for the baseline and proposed frameworks. While some works have explored aspects of game theoretic planning and intelligent systems validation separately, we combine each of these into a novel and comprehensive simulation pipeline. This integration demonstrates a dramatic improvement of the vector cost method over scalarization and offers an interpretable and generalizable framework for robotic behavioral planning. Code available at https://github.com/toazbenj/race_simulation. The video companion to this work is available at https://tinyurl.com/vectorcostvideo.

Vector Cost Behavioral Planning for Autonomous Robotic Systems with Contemporary Validation Strategies

TL;DR

The paper addresses robust multi-objective behavioral planning for autonomous robots by modeling decision-making as a vector cost bimatrix game and preserving objective structure under uncertainty. It advances a convex-optimization-based cost adjustment within a potential-game framework to enforce Nash equilibria that align with security policies, and it demonstrates that a radial-basis-like cost redesign improves convergence for higher-dimensional objective sets. The approach is validated through a circular racing scenario, leveraging SHAP for explainability and SEMBAS for boundary-focused sensitivity analysis, showing superior robustness and interpretability compared to scalarized baselines. This integrated V&V pipeline enhances transparency, robustness to weight perturbations, and practical applicability of multi-objective game-theoretic planning in autonomous systems.

Abstract

The vector cost bimatrix game is a method for multi-objective decision making that enables autonomous robotic systems to optimize for multiple goals at once while avoiding worst-case scenarios in neglected objectives. We expand this approach to arbitrary numbers of objectives and compare its performance to scalar weighted sum methods during competitive motion planning. Explainable Artificial Intelligence (XAI) software is used to aid in the analysis of high dimensional decision-making data. State-space Exploration of Multidimensional Boundaries using Adherence Strategies (SEMBAS) is applied to explore performance modes in the parameter space as a sensitivity study for the baseline and proposed frameworks. While some works have explored aspects of game theoretic planning and intelligent systems validation separately, we combine each of these into a novel and comprehensive simulation pipeline. This integration demonstrates a dramatic improvement of the vector cost method over scalarization and offers an interpretable and generalizable framework for robotic behavioral planning. Code available at https://github.com/toazbenj/race_simulation. The video companion to this work is available at https://tinyurl.com/vectorcostvideo.

Paper Structure

This paper contains 13 sections, 2 theorems, 14 equations, 10 figures, 2 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. Related Literature
  3. Contributions
  4. Problem Formulation
  5. Methods
  6. Cost Adjustment through Convex Optimization
  7. Conditions for Algorithm Convergence
  8. Cost Structure Design and Optimization
  9. Validation Tools and Algorithm Improvement Pipeline
  10. Results
  11. Tabular data and Feature Analysis
  12. Weight Sensitivity Analysis
  13. Conclusion

Key Result

Theorem 1

Given input matrices $C_1^1$ and $D_2$ and for any fixed set of weights $\Theta_1, \Theta_2$, the resulting policies $\{\tilde{\gamma}^s$, $\sigma^s\}$ form a pair of security policies for the bimatrix game $\tilde{D}_1, C_2$ and also a Nash equilibrium.

Figures (10)

  • Figure 1: Distances used for cost design
  • Figure 2: Linear cost structure
  • Figure 3: Radial basis cost structure
  • Figure 4: Simulation and validation pipeline
  • Figure 5: Spawning scenarios for grid search testing
  • ...and 5 more figures

Theorems & Definitions (6)

  • Theorem 1: Output of Algorithm \ref{['alg:policy select']}
  • Theorem 2: Required Cost Conditions
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4