Fast k-connectivity Restoration in Multi-Robot Systems for Robust Communication Maintenance

Maintaining a robust communication network plays an important role in the success of a multi-robot team jointly performing an optimization task. A key characteristic of a robust cooperative multi-robot system is the ability to repair the communication topology in the case of robot failure. In this paper, we focus on the Fast k-connectivity Restoration (FCR) problem, which aims to repair a network to make it k-connected with minimum robot movement. We develop a Quadratically Constrained Program (QCP) formulation of the FCR problem, which provides a way to optimally solve the problem, but cannot handle large instances due to high computational overhead. We therefore present a scalable algorithm, called EA-SCR, for the FCR problem using graph theoretic concepts. By conducting empirical studies, we demonstrate that the EA-SCR algorithm performs within 10 percent of the optimal while being orders of magnitude faster. We also show that EA-SCR outperforms existing solutions by 30 percent in terms of the FCR distance metric.

LAVA: Long-horizon Visual Action based Food Acquisition

Robotic Assisted Feeding (RAF) addresses the fundamental need for individuals with mobility impairments to regain autonomy in feeding themselves. The goal of RAF is to use a robot arm to acquire and transfer food to individuals from the table. Existing RAF methods primarily focus on solid foods, leaving a gap in manipulation strategies for semi-solid and deformable foods. This study introduces Long-horizon Visual Action (LAVA) based food acquisition of liquid, semisolid, and deformable foods. Long-horizon refers to the goal of "clearing the bowl" by sequentially acquiring the food from the bowl. LAVA employs a hierarchical policy for long-horizon food acquisition tasks. The framework uses high-level policy to determine primitives by leveraging ScoopNet. At the mid-level, LAVA finds parameters for primitives using vision. To carry out sequential plans in the real world, LAVA delegates action execution which is driven by Low-level policy that uses parameters received from mid-level policy and behavior cloning ensuring precise trajectory execution. We validate our approach on complex real-world acquisition trials involving granular, liquid, semisolid, and deformable food types along with fruit chunks and soup acquisition. Across 46 bowls, LAVA acquires much more efficiently than baselines with a success rate of 89 +/- 4% and generalizes across realistic plate variations such as different positions, varieties, and amount of food in the bowl. Code, datasets, videos, and supplementary materials can be found on our website.

Inverse Submodular Maximization with Application to Human-in-the-Loop Multi-Robot Multi-Objective Coverage Control

We consider a new type of inverse combinatorial optimization, Inverse Submodular Maximization (ISM), for human-in-the-loop multi-robot coordination. Forward combinatorial optimization, defined as the process of solving a combinatorial problem given the reward (cost)-related parameters, is widely used in multi-robot coordination. In the standard pipeline, the reward (cost)-related parameters are designed offline by domain experts first and then these parameters are utilized for coordinating robots online. What if we need to change these parameters by non-expert human supervisors who watch over the robots during tasks to adapt to some new requirements? We are interested in the case where human supervisors can suggest what actions to take, and the robots need to change the internal parameters based on such suggestions. We study such problems from the perspective of inverse combinatorial optimization, i.e., the process of finding parameters given solutions to the problem. Specifically, we propose a new formulation for ISM, in which we aim to find a new set of parameters that minimally deviate from the current parameters and can make the greedy algorithm output actions the same as those suggested by humans. We show that such problems can be formulated as a Mixed Integer Quadratic Program (MIQP). However, MIQP involves exponentially many binary variables, making it intractable for the existing solver when the problem size is large. We propose a new algorithm under the Branch $\&$ Bound paradigm to solve such problems. In numerical simulations, we demonstrate how to use ISM in multi-robot multi-objective coverage control, and we show that the proposed algorithm achieves significant advantages in running time and peak memory usage compared to directly using an existing solver.

From Words to Routes: Applying Large Language Models to Vehicle Routing

LLMs have shown impressive progress in robotics (e.g., manipulation and navigation) with natural language task descriptions. The success of LLMs in these tasks leads us to wonder: What is the ability of LLMs to solve vehicle routing problems (VRPs) with natural language task descriptions? In this work, we study this question in three steps. First, we construct a dataset with 21 types of single- or multi-vehicle routing problems. Second, we evaluate the performance of LLMs across four basic prompt paradigms of text-to-code generation, each involving different types of text input. We find that the basic prompt paradigm, which generates code directly from natural language task descriptions, performs the best for GPT-4, achieving 56% feasibility, 40% optimality, and 53% efficiency. Third, based on the observation that LLMs may not be able to provide correct solutions at the initial attempt, we propose a framework that enables LLMs to refine solutions through self-reflection, including self-debugging and self-verification. With GPT-4, our proposed framework achieves a 16% increase in feasibility, a 7% increase in optimality, and a 15% increase in efficiency. Moreover, we examine the sensitivity of GPT-4 to task descriptions, specifically focusing on how its performance changes when certain details are omitted from the task descriptions, yet the core meaning is preserved. Our findings reveal that such omissions lead to a notable decrease in performance: 4% in feasibility, 4% in optimality, and 5% in efficiency. Website: https://sites.google.com/view/words-to-routes/

AG-CVG: Coverage Planning with a Mobile Recharging UGV and an Energy-Constrained UAV

In this paper, we present an approach for coverage path planning for a team of an energy-constrained Unmanned Aerial Vehicle (UAV) and an Unmanned Ground Vehicle (UGV). Both the UAV and the UGV have predefined areas that they have to cover. The goal is to perform complete coverage by both robots while minimizing the coverage time. The UGV can also serve as a mobile recharging station. The UAV and UGV need to occasionally rendezvous for recharging. We propose a heuristic method to address this NP-Hard planning problem. Our approach involves initially determining coverage paths without factoring in energy constraints. Subsequently, we cluster segments of these paths and employ graph matching to assign UAV clusters to UGV clusters for efficient recharging management. We perform numerical analysis on real-world coverage applications and show that compared with a greedy approach our method reduces rendezvous overhead on average by 11.33\%. We demonstrate proof-of-concept with a team of a VOXL m500 drone and a Clearpath Jackal ground vehicle, providing a complete system from the offline algorithm to the field execution.

Decision-Oriented Intervention Cost Prediction for Multi-robot Persistent Monitoring

In this paper, we present a differentiable, decision-oriented learning technique for a class of vehicle routing problems. Specifically, we consider a scenario where a team of Unmanned Aerial Vehicles (UAVs) and Unmanned Ground Vehicles (UGVs) are persistently monitoring an environment. The UGVs are occasionally taken over by humans to take detours to recharge the depleted UAVs. The goal is to select routes for the UGVs so that they can efficiently monitor the environment while reducing the cost of interventions. The former is modeled as a monotone, submodular function whereas the latter is a linear function of the routes of the UGVs. We consider a scenario where the former is known but the latter depends on the context (e.g., wind and terrain conditions) that must be learned. Typically, we first learn to predict the cost function and then solve the optimization problem. However, the loss function used in prediction may be misaligned with our final goal of finding good routes. We propose a \emph{decision-oriented learning} framework that incorporates task optimization as a differentiable layer in the prediction phase. To make the task optimization (which is a non-monotone submodular function) differentiable, we propose the Differentiable Cost Scaled Greedy algorithm. We demonstrate the efficacy of the proposed framework through numerical simulations. The results show that the proposed framework can result in better performance than the traditional approach.

Where to Drop Sensors from Aerial Robots to Monitor a Surface-Level Phenomenon?

We consider the problem of routing a team of energy-constrained Unmanned Aerial Vehicles (UAVs) to drop unmovable sensors for monitoring a task area in the presence of stochastic wind disturbances. In prior work on mobile sensor routing problems, sensors and their carrier are one integrated platform, and sensors are assumed to be able to take measurements at exactly desired locations. By contrast, airdropping the sensors onto the ground can introduce stochasticity in the landing locations of the sensors. We focus on addressing this stochasticity in sensor locations from the path-planning perspective. Specifically, we formulate the problem (Multi-UAV Sensor Drop) as a variant of the Submodular Team Orienteering Problem with one additional constraint on the number of sensors on each UAV. The objective is to maximize the Mutual Information between the phenomenon at Points of Interest (PoIs) and the measurements that sensors will take at stochastic locations. We show that such an objective is computationally expensive to evaluate. To tackle this challenge, we propose a surrogate objective with a closed-form expression based on the expected mean and expected covariance of the Gaussian Process. We propose a heuristic algorithm to solve the optimization problem with the surrogate objective. The formulation and the algorithms are validated through extensive simulations.

Data-Driven Distributionally Robust Optimal Control with State-Dependent Noise

This paper introduces innovative data-driven techniques for estimating the noise distribution and KL divergence bound for distributionally robust optimal control (DROC). The proposed approach addresses the limitation of traditional DROC approaches that require known ambiguity sets for the noise distribution, our approach can learn these distributions and bounds in real-world scenarios where they may not be known a priori. To evaluate the effectiveness of our approach, a navigation problem involving a car-like robot under different noise distributions is used as a numerical example. The results demonstrate that DROC combined with the proposed data-driven approaches, what we call D3ROC, provide robust and efficient control policies that outperform the traditional iterative linear quadratic Gaussian (iLQG) control approach. Moreover, it shows the effectiveness of our proposed approach in handling different noise distributions. Overall, the proposed approach offers a promising solution to real-world DROC problems where the noise distribution and KL divergence bounds may not be known a priori, increasing the practicality and applicability of the DROC framework.

Decision-Oriented Learning with Differentiable Submodular Maximization for Vehicle Routing Problem

We study the problem of learning a function that maps context observations (input) to parameters of a submodular function (output). Our motivating case study is a specific type of vehicle routing problem, in which a team of Unmanned Ground Vehicles (UGVs) can serve as mobile charging stations to recharge a team of Unmanned Ground Vehicles (UAVs) that execute persistent monitoring tasks. {We want to learn the mapping from observations of UAV task routes and wind field to the parameters of a submodular objective function, which describes the distribution of landing positions of the UAVs .} Traditionally, such a learning problem is solved independently as a prediction phase without considering the downstream task optimization phase. However, the loss function used in prediction may be misaligned with our final goal, i.e., a good routing decision. Good performance in the isolated prediction phase does not necessarily lead to good decisions in the downstream routing task. In this paper, we propose a framework that incorporates task optimization as a differentiable layer in the prediction phase. Our framework allows end-to-end training of the prediction model without using engineered intermediate loss that is targeted only at the prediction performance. In the proposed framework, task optimization (submodular maximization) is made differentiable by introducing stochastic perturbations into deterministic algorithms (i.e., stochastic smoothing). We demonstrate the efficacy of the proposed framework using synthetic data. Experimental results of the mobile charging station routing problem show that the proposed framework can result in better routing decisions, e.g. the average number of UAVs recharged increases, compared to the prediction-optimization separate approach.

Risk-aware Resource Allocation for Multiple UAVs-UGVs Recharging Rendezvous

We study a resource allocation problem for the cooperative aerial-ground vehicle routing application, in which multiple Unmanned Aerial Vehicles (UAVs) with limited battery capacity and multiple Unmanned Ground Vehicles (UGVs) that can also act as a mobile recharging stations need to jointly accomplish a mission such as persistently monitoring a set of points. Due to the limited battery capacity of the UAVs, they sometimes have to deviate from their task to rendezvous with the UGVs and get recharged. Each UGV can serve a limited number of UAVs at a time. In contrast to prior work on deterministic multi-robot scheduling, we consider the challenge imposed by the stochasticity of the energy consumption of the UAV. We are interested in finding the optimal recharging schedule of the UAVs such that the travel cost is minimized and the probability that no UAV runs out of charge within the planning horizon is greater than a user-defined tolerance. We formulate this problem ({Risk-aware Recharging Rendezvous Problem (RRRP))} as an Integer Linear Program (ILP), in which the matching constraint captures the resource availability constraints and the knapsack constraint captures the success probability constraints. We propose a bicriteria approximation algorithm to solve RRRP. We demonstrate the effectiveness of our formulation and algorithm in the context of one persistent monitoring mission.