We study informative path planning for active regression in Gaussian Processes (GP). Here, a resource constrained robot team collects measurements of an unknown function, assumed to be a sample from a GP, with the goal of minimizing the trace of the$M$-weighted expected squared estimation error covariance (where$M$is a positive semidefinite matrix) resulting from the GP posterior mean. While greedy heuristics are a popular solution in the case of length constrained paths, it remains a challenge to computeoptimalsolutions in the discrete setting subject to routing constraints. We show that this challenge is surprisingly easy to circumvent. Using the optimality of the posterior mean for a class of functions of the squared loss yields an exact formulation as a mixed integer program. We demonstrate that this approach finds optimal solutions in a variety of settings in seconds and when terminated early, it finds sub-optimal solutions of higher quality than existing heuristics.

Many problems in robotics seek to simultaneously optimize several competing objectives. A conventional approach 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 multiobjective problem. However, finding an accurate representation of a Pareto front remains an important challenge. Uniformly spaced weights are often inefficient and do not provide error bounds. We address the problem of computing a finite set of weights whose optimal solutions closely approximate the solution of any other weight vector. To this end, we prove fundamental properties of the optimal cost as a function of the weight vector. We propose an algorithm that greedily adds the weight vector least-represented by the current set, and provide bounds on the regret. We extend our method to include suboptimal solvers for the scalarized optimization, and handle stochastic inputs to the planning problem. Finally, we illustrate that the proposed approach significantly outperforms baseline approaches for different robot planning problems with varying numbers of objective functions.

We study the problem of finding statistically distinct plans for stochastic task assignment problems such as online multi-robot pickup and delivery (MRPD) when facing multiple competing objectives. In many real-world settings robot fleets do not only need to fulfil delivery requests, but also have to consider auxiliary objectives such as energy efficiency or avoiding human-centered work spaces. We pose MRPD as a multi-objective optimization problem where the goal is to find MRPD policies that yield different trade-offs between given objectives. There are two main challenges: 1) MRPD is computationally hard, which limits the number of trade-offs that can reasonably be computed, and 2) due to the random task arrivals, one needs to consider statistical variance of the objective values in addition to the average. We present an adaptive sampling algorithm that finds a set of policies which i) are approximately optimal, ii) approximate the set of all optimal solutions, and iii) are statistically distinguishable. We prove completeness and adapt a state-of-the-art MRPD solver to the multi-objective setting for three example objectives. In a series of simulation experiments we demonstrate the advantages of the proposed method compared to baseline approaches and show its robustness in a sensitivity analysis. The approach is general and could be adapted to other multi-objective task assignment and planning problems under uncertainty.

We study the sample placement and shortest tour problem for robots tasked with mapping environmental phenomena modeled as stationary random fields. The objective is to minimize the resources used (samples or tour length) while guaranteeing estimation accuracy. We give approximation algorithms for both problems in convex environments. These improve previously known results, both in terms of theoretical guarantees and in simulations. In addition, we disprove an existing claim in the literature on a lower bound for a solution to the sample placement problem.

Enabling a broader range of users to efficiently deploy autonomous mobile robots requires intuitive frameworks for specifying a robot's task and behaviour. We present a novel approach using learning from corrections (LfC), where a user is iteratively presented with a solution to a motion planning problem. Users might have preferences about parts of a robot's environment that are suitable for robot traffic or that should be avoided as well as preferences on the control actions a robot can take. The robot is initially unaware of these preferences; thus, we ask the user to provide a correction to the presented path. We assume that the user evaluates paths based on environment and motion features. From a sequence of corrections we learn weights for these features, which are then considered by the motion planner, resulting in future paths that better fit the user's preferences. We prove completeness of our algorithm and demonstrate its performance in simulations. Thereby, we show that the learned preferences yield good results not only for a set of training tasks but also for test tasks, as well as for different types of user behaviour.

We study active preference learning as a frame-work for intuitively specifying the behaviour of autonomous robots. A user chooses the preferred behaviour from a set of alternatives, from which the robot learns the user's preferences, modeled as a parameterized cost function. Previous approaches present users with alternatives that minimize the uncertainty over the parameters of the cost function. However, different parameters might lead to the same optimal behaviour; as a consequence the solution space is more structured than the parameter space. We exploit this by proposing a query selection that greedily reduces the maximum error ratio over the solution space. In simulations we demonstrate that the proposed approach outperforms other state of the art techniques in both learning efficiency and ease of queries for the user. Finally, we show that evaluating the learning based on the similarities of solutions instead of the similarities of weights allows for better predictions for different scenarios.

In this paper we develop an approach for learning user preferences for complex task specifications through human-robot interaction. We consider the problem of planning robot motion in a known environment, but where a user has specified additional spatial and temporal constraints on allowable robot motions. To illustrate the impact of the user's constraints on performance, we iteratively present users with alternative solutions on an interface. The user provides a ranking of alternate paths, and from this we learn about the importance of different constraints. This allows for an accessible method for specifying complex robot tasks. We present an algorithm that iteratively builds a set of constraints on the relative importance of each user constraint, and prove that with sufficient interaction, the algorithm determines a user-optimal path. We demonstrate the practical performance by simulating realistic material transport scenarios in industrial facilities.