arXiv subjects

Paul Trodden

Publications and source records attributed to Paul Trodden.

10 recordsLinked to original sources

arXiv2026

Scalable Multi-Agent Maze Traversal with Local Communication

Cave networks, pipe systems, and similar maze-like environments pose significant challenges for multi-agent navigation in unknown settings with limited communication. We propose a distributed algorithm that enables agents to collectively traverse an unknown, possibly cyclic graph. Agents enter sequentially at a designated start node and are tasked to localize and reach an undisclosed goal while avoiding collisions. They coordinate via local communication using leader-follower relationships and leader switching. At any moment in time, exploration is performed by only one of the agents, which runs a single-agent maze solver. We prove that the algorithm is complete, that its makespan is asymptotically equivalent (in the number of agents) to that of an optimal full-knowledge strategy, and derive its time and space complexity. Simulations with up to $625$ agents show a decreasing average sum-of-fuels as the number of agents increases and demonstrate that the proposed approach outperforms a na\"ive baseline in which all agents independently execute the single-agent solver.

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arXiv2026

When expectation fails: stochastic MPC of linear systems with random input losses

We consider stochastic model predictive control (MPC) for constrained linear systems subject to multiplicative binary input uncertainty, motivated by applications such as networked control with packet losses and intermittent actuation. A common approach in this setting replaces the stochastic dynamics with their expectation, yielding tractable formulations that admit standard terminal ingredients and stability guarantees in expectation. We show that such formulations can exhibit structural properties that differ fundamentally from those of deterministic MPC and may be misleading as indicators of realized closed-loop behaviour. In particular, the expected value function is not necessarily monotonic in the prediction horizon, and value function-based inner approximations of the region of attraction may deteriorate as the horizon increases. Furthermore, we establish a probabilistic comparison with certainty-equivalent (optimistic) MPC, showing that the latter can ensure a strictly positive probability of recursive feasibility in situations where stochastic MPC certifies feasibility but fails with probability one. These results highlight inherent limitations of expectation-based stochastic MPC for systems with multiplicative binary uncertainty and motivate a re-examination of how stochasticity is incorporated into constrained predictive control design for such systems.

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arXiv2025

Design for One, Deploy for Many: Navigating Tree Mazes with Multiple Agents

Maze-like environments, such as cave and pipe networks, pose unique challenges for multiple robots to coordinate, including communication constraints and congestion. To address these challenges, we propose a distributed multi-agent maze traversal algorithm for environments that can be represented by acyclic graphs. It uses a leader-switching mechanism where one agent, assuming a head role, employs any single-agent maze solver while the other agents each choose an agent to follow. The head role gets transferred to neighboring agents where necessary, ensuring it follows the same path as a single agent would. The multi-agent maze traversal algorithm is evaluated in simulations with groups of up to 300 agents, various maze sizes, and multiple single-agent maze solvers. It is compared against strategies that are na\"ive, or assume either global communication or full knowledge of the environment. The algorithm outperforms the na\"ive strategy in terms of makespan and sum-of-fuel. It is superior to the global-communication strategy in terms of makespan but is inferior to it in terms of sum-of-fuel. The findings suggest it is asymptotically equivalent to the full-knowledge strategy with respect to either metric. Moreover, real-world experiments with up to 20 Pi-puck robots confirm the feasibility of the approach.

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arXiv2025

On the Limits of Robust Control Under Adversarial Disturbances

This paper addresses a fundamental and important question in control: under what conditions does there fail to exist a robust control policy that keeps the state of a constrained linear system within a target set, despite bounded disturbances? This question has practical implications for actuator and sensor specification, feasibility analysis for reference tracking, and the design of adversarial attacks in cyber-physical systems. While prior research has predominantly focused on using optimization to compute control-invariant sets to ensure feasible operation, our work complements these approaches by characterizing explicit sufficient conditions under which robust control is fundamentally infeasible. Specifically, we derive novel closed-form, algebraic expressions that relate the size of a disturbance set -- modelled as a scaled version of a basic shape -- to the system's spectral properties and the geometry of the constraint sets.

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arXiv2025

NISE-PE Constraint: Data-Driven Predictive Control with Persistence of Excitation

Persistence of excitation (PE) is an important requirement for the successful operation of data-driven predictive control, as it ensures that the input-output data contains sufficient information about the underlying system dynamics. Nonetheless, this property is usually assumed rather than guaranteed. This paper introduces a novel data-driven predictive control formulation that maintains PE. The technical development that allows this is the characterisation of the nonexciting input set (NIS), i.e., the set of inputs that lead to loss of PE, and the consequent derivation of a pair of disjoint, linear inequality constraints on the input, termed NIS exclusion PE (NIS-PE) constraint, that, if satisfied, maintain PE. When used in a predictive control formulation, these constraints lead to a mixed-integer optimal control problem with a single binary variable or, equivalently, a pair of disjoint quadratic programming problems that can be efficiently and reliably solved. Numerical examples show how these constraints are able to maintain PE during the controller's operation, resulting in improved performance over conventional approaches for both time-invariant and time-varying systems.

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arXiv2024

On the Benefits of Robot Platooning for Navigating Crowded Environments

This paper studies how groups of robots can effectively navigate through a crowd of agents. It quantifies the performance of platooning and less constrained, greedy strategies, and the extent to which these strategies disrupt the crowd agents. Three scenarios are considered: (i) passive crowds, (ii) counter-flow crowds, and (iii) perpendicular-flow crowds. Through simulations consisting of up to 200 robots, we show that for navigating passive and counter-flow crowds, the platooning strategy is less disruptive and more effective in dense crowds than the greedy strategy, whereas for navigating perpendicular-flow crowds, the greedy strategy outperforms the platooning strategy in either aspect. Moreover, we propose an adaptive strategy that can switch between platooning and greedy behavioral states, and demonstrate that it combines the strengths of both strategies in all the scenarios considered.

cs.RO↗

arXiv2016

Distributed MPC: Guaranteeing Global Stabilizability from Locally Designed Tubes

This paper studies a fundamental relation that exists between stabilizability assumptions usually employed in distributed model predictive control implementations, and the corresponding notions of invariance implicit in such controllers. The relation is made explicit in the form of a theorem that presents sufficient conditions for global stabilizability. It is shown that constraint admissibility of local robust controllers is sufficient for the global closed-loop system to be stable, and how these controllers are related to more complex forms of control such as tube-based distributed model predictive control implementations.

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arXiv2016

Distributed Model Predictive Control Using a Chain of Tubes

A new distributed MPC algorithm for the regulation of dynamically coupled subsystems is presented in this paper. The current control action is computed via two robust controllers working in a nested fashion. The inner controller builds a nominal reference trajectory from a decentralized perspective. The outer controller uses this information to take into account the effects of the coupling and generate a distributed control action. The tube-based approach to robustness is employed. A supplementary constraint is included in the outer optimization problem to provide recursive feasibility of the overall controller

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arXiv2015

Persistently Exciting Tube MPC

This paper presents a new approach to deal with the dual problem of system identification and regulation. The main feature consists of breaking the control input to the system into a regulator part and a persistently exciting part. The former is used to regulate the plant using a robust MPC formulation, in which the latter is treated as a bounded additive disturbance. The identification process is executed by a simple recursive least squares algorithm. In order to guarantee sufficient excitation for the identification, an additional non-convex constraint is enforced over the persistently exciting part.

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arXiv2015

A One-step Approach to Computing a Polytopic Robust Positively Invariant Set

A procedure and theoretical results are presented for the problem of determining a minimal robust positively invariant (RPI) set for a linear discrete-time system subject to unknown, bounded disturbances. The procedure computes, via the solving of a single LP, a polytopic RPI set that is minimal with respect to the family of RPI sets generated from a finite number of inequalities with pre-defined normal vectors.

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