Sample-Based Hybrid Mode Control: Asymptotically Optimal Switching of Algorithmic and Non-Differentiable Control Modes

2025-10-21

AI Summary

This work addresses hybrid-mode control problems involving non-differentiable systems coexisting with algorithmic controllers. We propose a sampling-based integer optimization framework that unifies the modeling of control mode selection, switching instants, and dwell times. Unlike conventional continuous optimization or heuristic switching strategies, our approach performs asymptotically optimal mode sequence planning directly in the integer domain, balancing long-horizon task objectives with high-frequency real-time responsiveness. Methodologically, we integrate hybrid dynamical modeling, non-differentiable control synthesis, and efficient discrete search—eliminating reliance on gradient information. The framework is validated on a real robotic platform, demonstrating significant advantages in compositional complex behavior generation, adaptation to dynamic environments, and formal performance guarantees.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

This paper investigates a sample-based solution to the hybrid mode control problem across non-differentiable and algorithmic hybrid modes. Our approach reasons about a set of hybrid control modes as an integer-based optimization problem where we select what mode to apply, when to switch to another mode, and the duration for which we are in a given control mode. A sample-based variation is derived to efficiently search the integer domain for optimal solutions. We find our formulation yields strong performance guarantees that can be applied to a number of robotics-related tasks. In addition, our approach is able to synthesize complex algorithms and policies to compound behaviors and achieve challenging tasks. Last, we demonstrate the effectiveness of our approach in real-world robotic examples that require reactive switching between long-term planning and high-frequency control.

Problem

• Solving hybrid mode control with non-differentiable and algorithmic modes
• Optimizing mode selection, switching timing, and duration parameters
• Enabling reactive switching between planning and control in robotics

Innovation

• Sample-based optimization for hybrid mode switching
• Integer-based formulation for mode selection and timing
• Efficient search in integer domain for robotics tasks