Many problems in robotics seek to simultaneously optimize several competing objectives under constraints. A conventional approach to solving such multi-objective optimization problems is to create a single cost function comprised of the weighted sum of the individual objectives. Solutions to this scalarized optimization problem are Pareto optimal solutions to the original multi-objective problem. However, finding an accurate representation of a Pareto front remains an important challenge. Using uniformly spaced weight vectors is often inefficient and does not provide error bounds. Thus, we address the problem of computing a finite set of weight vectors such that for any other weight vector, there exists an element in the set whose error compared to optimal is minimized. To this end, we prove fundamental properties of the optimal cost as a function of the weight vector, including its continuity and concavity. Using these, we propose an algorithm that greedily adds the weight vector least-represented by the current set, and provide bounds on the error. Finally, we illustrate that the proposed approach significantly outperforms uniformly distributed weights for different robot planning problems with varying numbers of objective functions.

No abstract

No abstract

In this paper, we revisit the distributed coverage control problem with multiple robots on both metric graphs and in non-convex continuous environments. Traditionally, the solutions provided for this problem converge to a locally optimal solution with no guarantees on the quality of the solution. We consider sub-additive sensing functions, which capture the scenarios where sensing an event requires the robot to visit the event location. For these sensing functions, we provide the first constant factor approximation algorithms for the distributed coverage problem. The approximation results require twice the conventional communication range in the existing coverage algorithms. However, we show through extensive simulation results that the proposed approximation algorithms outperform several existing algorithms in convex, non-convex continuous, and discrete environments even with the conventional communication ranges. Moreover, the proposed algorithms match the stateof-the-art centralized algorithms in the solution quality.

Mobile robots are often tasked with repeatedly navigating through an environment whose traversability changes over time. These changes may exhibit some hidden structure, which can be learned. Many studies consider reactive algorithms for online planning, however, these algorithms do not take advantage of the past executions of the navigation task for future tasks. In this paper, we formalize the problem of minimizing the total expected cost to perform multiple start-togoal navigation tasks on a roadmap by introducing the Learned Reactive Planning Problem. We propose a method that captures information from past executions to learn a motion policy to handle obstacles that the robot has seen before. We propose the LAMP framework, which integrates the generated motion policy with an existing navigation stack. Finally, an extensive set of experiments in simulated and real-world environments show that the proposed method outperforms the state-of-theart algorithms by 10% to 40% in terms of expected time to travel from start to goal. We also evaluate the robustness of the proposed method in the presence of localization and mapping errors on a real robot.