Michael Morin

Constraint programming for path planning with uncertainty: solving the optimal search path problem

The optimal search path (OSP) problem is a single-sided detection search problem where the location and the detectability of a moving object are uncertain. A solution to this

The Markov Transition Constraint

\mathcal{NP}

A hybrid algorithm for coverage path planning with imperfect sensors

-hard problem is a path on a graph that maximizes the probability of finding an object that moves according to a known motion model. We developed constraint programming models to solve this probabilistic path planning problem for a single indivisible searcher. These models include a simple but powerful branching heuristic as well as strong filtering constraints. We present our experimentation and compare our results with existing results in the literature. The OSP problem is particularly interesting in that it generalizes to various probabilistic search problems such as intruder detection, malicious code identification, search and rescue, and surveillance.

Machine learning-based metamodels for sawing simulation

We introduce a novel global Markov transition constraint (Mtc) to model finite state homogeneous Markov chains. We present two algorithms to filter the variable domains representing the imprecise probability distributions over the state space of the chain. The first filtering algorithm is based on the fractional knapsack problem and the second filtering algorithm is based on linear programming. Both of our filtering algorithms compare favorably to the filtering performed by solvers when decomposing an Mtc into arithmetic constraints. Cases where the fractional knapsack decomposition enforces bounds consistency are discussed whereas the linear programming filtering always perform bounds consistency. We use the Mtc constraint to model and solve a problem of path planning under uncertainty.

Bounding an Optimal Search Path with a Game of Cop and Robber on Graphs

We are interested in the coverage path planning problem with imperfect sensors, within the context of robotics for mine countermeasures. In the studied problem, an autonomous underwater vehicle (AUV) equipped with sonar surveys the bottom of the ocean searching for mines. We use a cellular decomposition to represent the ocean floor by a grid of uniform square cells. The robot scans a fixed number of cells sideways with a varying probability of detection as a function of distance and of seabed type. The goal is to plan a path that achieves the minimal required coverage in each cell while minimizing the total traveled distance and the total number of turns. We propose an off-line hybrid algorithm based on dynamic programming and on a traveling salesman problem reduction. We present experimental results and show that our algorithms performance is superior to published results in terms of path quality and computational time, which makes it possible to implement the algorithm in an AUV.

Intruder alert! Optimization models for solving the mobile robot graph-clear problem

We use machine learning to generate metamodels for sawing simulation. Simulation is widely used in the wood industry for decision making. These simulators are particular since their response for a given input is a structured object, i.e., a basket of lumbers. We demonstrate how we use simple machine learning algorithms (e.g., a tree) to obtain a good approximation of the simulators response. The generated metamodels are guaranteed to output physically realistic baskets (i.e., there exists at least one log that can produce the basket). We also propose to use kernel ridge regression. While having the power to exploit the structure of a basket, it can predict previously unseen baskets. We finally evaluate the impact of possibly predicting unrealistic baskets using ridge regression jointly with a nearest neighbor approach in the output space. All metamodels are evaluated using standard machine learning metrics and novel metrics especially designed for the problem.

The ant search algorithm: an ant colony optimization algorithm for the optimal searcher path problem with visibility

In search theory, the goal of the Optimal Search Path OSP problem is to find a finite length path maximizing the probability that a searcher detects a lost wanderer on a graph. We propose to bound the probability of finding the wanderer in the remaining search time by relaxing the problem into a stochastic game of cop and robber from graph theory. We discuss the validity of this bound and demonstrate its effectiveness on a constraint programming model of the problem. Experimental results show how our novel bound compares favorably to the DMEAN bound from the literature, a state-of-the-art bound based on a relaxation of the OSP into a longest path problem.

The optimal searcher path problem with a visibility criterion in discrete time and space

We develop optimization approaches to the graph-clear problem, a pursuit-evasion problem where mobile robots must clear a facility of intruders. The objective is to minimize the number of robots required. We contribute new formal results on progressive and contiguous assumptions and their impact on algorithm completeness. We present mixed-integer linear programming and constraint programming models, as well as new heuristic variants for the problem, comparing them to previously proposed heuristics. Our empirical work indicates that our heuristic variants improve on those from the literature, that constraint programming finds better solutions than the heuristics in run-times reasonable for the application, and that mixed-integer linear programming is superior for proving optimality. Given their performance and the appeal of the model-and-solve framework, we conclude that the proposed optimization methods are currently the most suitable for the graph-clear problem.

Towards a knowledge-based system prototype for aeronautical Search and Rescue operations

In the first part of this paper, we present the Optimal Searcher Path problem with Visibility, a novel path planning approach that models inter-region visibility and that uses concepts from search theory to model uncertainty on the goals (i.e., the search object) detectability and location In the second part, we introduce the Ant Search algorithm, a solving technique based on ant colony optimization Our results, when compared with a general mixed-integer programming model and solver, show that Ant Search is a promising technique for handling this particular complex problem.