Autonomously performing tasks often requires robots to plan high-level discrete actions and continuous low-level motions to realize them. Previous TAMP algorithms have focused mainly on computational performance, completeness, or optimality by making the problem tractable through simplifications and abstractions. However, this comes at the cost of the resulting plans potentially failing to account for the dynamics or complex contacts necessary to reliably perform the task when object manipulation is required. Additionally, approaches that ignore effects of the low-level controllers may not obtain optimal or feasible plan realizations for the real system. We investigate the use of a GPU-parallelized physics simulator to compute realizations of plans with motion controllers, explicitly accounting for dynamics, and considering contacts with the environment. Using cross-entropy optimization, we sample the parameters of the controllers, or actions, to obtain low-cost solutions. Since our approach uses the same controllers as the real system, the robot can directly execute the computed plans. We demonstrate our approach for a set of tasks where the robot is able to exploit the environment's geometry to move an object.

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 multi-objective 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.

When designing a motion planner for autonomous robots there are usually multiple objectives to be considered. However, a cost function that yields the desired trade-off between objectives is not easily obtainable. A common technique across many applications is to use a weighted sum of relevant objective functions and then carefully adapt the weights. However, this approach may not find all relevant trade-offs even in simple planning problems. Thus, we study an alternative method based on a weighted maximum of objectives. Such a cost function is more expressive than the weighted sum, and we show how it can be deployed in both continuous-and discrete-space motion planning problems. We propose a novel path planning algorithm for the proposed cost function and establish its correctness, and present heuristic adaptations that yield a practical runtime. In extensive simulation experiments, we demonstrate that the proposed cost function and algorithm are able to find a wider range of trade-offs between objectives (i.e., Pareto-optimal solutions) for various planning problems, showcasing its advantages in practice.

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.

Reward learning is a highly active area of research in human-robot interaction (HRI), allowing a broad range of users to specify complex robot behaviour. Experiments with simulated user input play a major role in the development and evaluation of reward learning algorithms due to the availability of a ground truth. In this paper, we review measures for evaluating reward learning algorithms used in HRI, most of which fall into two classes. In a theoretical worst case analysis and several examples, we show that both classes of measures can fail to effectively indicate how good the learned robot behaviour is. Thus, our work contributes to the characterization of sim-to-real gaps of reward learning in HRI.

We study the problem of deploying a fleet of mobile robots to service tasks that arrive stochastically over time and at random locations in an environment. This is known as the Dynamic Vehicle Routing Problem (DVRP) and requires robots to allocate incoming tasks among themselves and find an optimal sequence for each robot. State-of-the-art approaches only consider average wait times and focus on high-load scenarios where the arrival rate of tasks approaches the limit of what can be handled by the robots while keeping the queue of unserviced tasks bounded, i.e., stable. To ensure stability, these approaches repeatedly compute minimum distance tours over a set of newly arrived tasks. This letter is aimed at addressing the missing policies for moderate-load scenarios, where quality of service can be improved by prioritizing long-waiting tasks. We introduce a novel DVRP policy based on a cost function that takes the p-norm over accumulated wait times and show it guarantees stability even in high-load scenarios. We demonstrate that the proposed policy outperforms the state-of-the-art in both mean and 95th percentile wait times in moderate-load scenarios through simulation experiments in the Euclidean plane as well as using real-world data for city scale service requests.