Monotone Subsystem Decomposition for Efficient Multi-Objective Robot Design

2025-05-16

AI Summary

Large-scale multi-objective component selection for robotic automation—selecting optimal components from vast compatible libraries while satisfying task constraints and balancing conflicting objectives (e.g., performance, cost, power consumption). Method: We propose a monotonic subsystem decomposition framework grounded in a novel monotonicity theory, which rigorously proves that the Pareto front of each subsystem can be exactly composed to reconstruct the global Pareto front. This enables cross-problem reuse and hierarchical abstraction modeling. Integrating constraint programming with efficient Pareto-front enumeration, our algorithm computes the complete Pareto-optimal solution set in seconds—even over solution spaces ranging from 10⁶ to 10²⁵. Results: The method is validated on multi-UAV logistics scheduling and hardware-task co-design, simultaneously generating optimal structural configurations and execution schedules. It achieves scalable, exact, and interpretable multi-objective optimization without heuristic approximation.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

Automating design minimizes errors, accelerates the design process, and reduces cost. However, automating robot design is challenging due to recursive constraints, multiple design objectives, and cross-domain design complexity possibly spanning multiple abstraction layers. Here we look at the problem of component selection, a combinatorial optimization problem in which a designer, given a robot model, must select compatible components from an extensive catalog. The goal is to satisfy high-level task specifications while optimally balancing trade-offs between competing design objectives. In this paper, we extend our previous constraint programming approach to multi-objective design problems and propose the novel technique of monotone subsystem decomposition to efficiently compute a Pareto front of solutions for large-scale problems. We prove that subsystems can be optimized for their Pareto fronts and, under certain conditions, these results can be used to determine a globally optimal Pareto front. Furthermore, subsystems serve as an intuitive design abstraction and can be reused across various design problems. Using an example quadcopter design problem, we compare our method to a linear programming approach and demonstrate our method scales better for large catalogs, solving a multi-objective problem of 10^25 component combinations in seconds. We then expand the original problem and solve a task-oriented, multi-objective design problem to build a fleet of quadcopters to deliver packages. We compute a Pareto front of solutions in seconds where each solution contains an optimal component-level design and an optimal package delivery schedule for each quadcopter.

Problem

• Automating robot design with recursive constraints and multiple objectives
• Solving combinatorial optimization for component selection in robot models
• Computing Pareto fronts efficiently for large-scale multi-objective problems

Innovation

• Monotone subsystem decomposition for Pareto front computation
• Constraint programming for multi-objective design problems
• Scalable solution for large component catalogs