Effectiveness of Local Search for Geometric Optimization

What is the effectiveness of local search algorithms for geometric problems in the plane? We prove that local search with neighborhoods of magnitude 1/epsilon^c is an approximation scheme for the following problems in the Euclidean plane: TSP with random inputs, Steiner tree with random inputs, uniform facility location (with worst case inputs), and bicriteria k-median (also with worst case inputs). The randomness assumption is necessary for TSP

A genetic algorithm for mobile robot localization using ultrasonic sensors

A mobile robot requires the perception of its local environment for position estimation. Ultrasonic range data provide a robust description of the local environment for navigation. This article presents an ultrasonic sensor localization system for autonomous mobile robot navigation in an indoor semi-structured environment. The proposed algorithm is based upon an iterative non-linear filter, which utilizes matches between observed geometric beacons and an a-priori map of beacon locations, to correct the position and orientation of the vehicle. A non-linear filter based on a genetic algorithm as an emerging optimization method to search for optimal positions is described. The resulting self-localization module has been integrated successfully in a more complex navigation system. Experiments demonstrate the effectiveness of the proposed method in real world applications.Publicad

The Unreasonable Success of Local Search: Geometric Optimization

What is the effectiveness of local search algorithms for geometric problems in the plane? We prove that local search with neighborhoods of magnitude $1/\epsilon^c$ is an approximation scheme for the following problems in the Euclidian plane: TSP with random inputs, Steiner tree with random inputs, facility location (with worst case inputs), and bicriteria $k$-median (also with worst case inputs). The randomness assumption is necessary for TSP

Reinforcement learning based local search for grouping problems: A case study on graph coloring

Grouping problems aim to partition a set of items into multiple mutually disjoint subsets according to some specific criterion and constraints. Grouping problems cover a large class of important combinatorial optimization problems that are generally computationally difficult. In this paper, we propose a general solution approach for grouping problems, i.e., reinforcement learning based local search (RLS), which combines reinforcement learning techniques with descent-based local search. The viability of the proposed approach is verified on a well-known representative grouping problem (graph coloring) where a very simple descent-based coloring algorithm is applied. Experimental studies on popular DIMACS and COLOR02 benchmark graphs indicate that RLS achieves competitive performances compared to a number of well-known coloring algorithms

The Design and Implementation of a Bayesian CAD Modeler for Robotic Applications

We present a Bayesian CAD modeler for robotic applications. We address the problem of taking into account the propagation of geometric uncertainties when solving inverse geometric problems. The proposed method may be seen as a generalization of constraint-based approaches in which we explicitly model geometric uncertainties. Using our methodology, a geometric constraint is expressed as a probability distribution on the system parameters and the sensor measurements, instead of a simple equality or inequality. To solve geometric problems in this framework, we propose an original resolution method able to adapt to problem complexity. Using two examples, we show how to apply our approach by providing simulation results using our modeler

DeepICP: An End-to-End Deep Neural Network for 3D Point Cloud Registration

We present DeepICP - a novel end-to-end learning-based 3D point cloud registration framework that achieves comparable registration accuracy to prior state-of-the-art geometric methods. Different from other keypoint based methods where a RANSAC procedure is usually needed, we implement the use of various deep neural network structures to establish an end-to-end trainable network. Our keypoint detector is trained through this end-to-end structure and enables the system to avoid the inference of dynamic objects, leverages the help of sufficiently salient features on stationary objects, and as a result, achieves high robustness. Rather than searching the corresponding points among existing points, the key contribution is that we innovatively generate them based on learned matching probabilities among a group of candidates, which can boost the registration accuracy. Our loss function incorporates both the local similarity and the global geometric constraints to ensure all above network designs can converge towards the right direction. We comprehensively validate the effectiveness of our approach using both the KITTI dataset and the Apollo-SouthBay dataset. Results demonstrate that our method achieves comparable or better performance than the state-of-the-art geometry-based methods. Detailed ablation and visualization analysis are included to further illustrate the behavior and insights of our network. The low registration error and high robustness of our method makes it attractive for substantial applications relying on the point cloud registration task.Comment: 10 pages, 6 figures, 3 tables, typos corrected, experimental results updated, accepted by ICCV 201

A Robotic CAD System using a Bayesian Framework

We present in this paper a Bayesian CAD system for robotic applications. We address the problem of the propagation of geometric uncertainties and how esian CAD system for robotic applications. We address the problem of the propagation of geometric uncertainties and how to take this propagation into account when solving inverse problems. We describe the methodology we use to represent and handle uncertainties using probability distributions on the system's parameters and sensor measurements. It may be seen as a generalization of constraint-based approaches where we express a constraint as a probability distribution instead of a simple equality or inequality. Appropriate numerical algorithms used to apply this methodology are also described. Using an example, we show how to apply our approach by providing simulation results using our CAD system