The Moving Target Traveling Salesman Problem (MT-TSP) seeks a trajectory that intercepts several moving targets, within a particular time window for each target. When generic nonlinear target trajectories or kinematic constraints on the agent are present, no prior algorithm guarantees convergence to an optimal MT-TSP solution. Therefore, we introduce the Iterated Random Generalized (IRG) TSP framework. The idea behind IRG is to alternate between randomly sampling a set of agent configuration-time points, corresponding to interceptions of targets, and finding a sequence of interception points by solving a generalized TSP (GTSP). This alternation asymptotically converges to the optimum. We introduce two parallel algorithms within the IRG framework. The first algorithm, IRG-PGLNS, solves GTSPs using PGLNS, our parallelized extension of state-of-the-art solver GLNS. The second algorithm, Parallel Communicating GTSPs (PCG), solves GTSPs for several sets of points simultaneously. We present numerical results for three MT-TSP variants: one where intercepting a target only requires coming within a particular distance, another where the agent is a variable-speed Dubins car, and a third where the agent is a robot arm. We show that IRG-PGLNS and PCG converge faster than a baseline based on prior work. We further validate our framework with physical robot experiments.

The moving target traveling salesman problem with obstacles (MT-TSP-O) seeks an obstacle-free trajectory for an agent that intercepts a given set of moving targets, each within specified time windows, and returns to the agent's starting position. Each target moves with a constant velocity within its time windows, and the agent has a speed limit no smaller than any target's speed. We present FMC*-TSP, the first complete and bounded-suboptimal algorithm for the MT-TSP-O, and results for an agent whose configuration space is$\mathbb{R}^{3}$. Our algorithm interleaves a high-level search and a lowlevel search, where the high-level search solves a generalized traveling salesman problem with time windows (GTSP-TW) to find a sequence of targets and corresponding time windows for the agent to visit. Given such a sequence, the low-level search then finds an associated agent trajectory. To solve the low-level planning problem, we develop a new algorithm called FMC*, which finds a shortest path on a graph of convex sets (GCS) via implicit graph search and pruning techniques specialized for problems with moving targets. We test FMC*-TSP on 280 problem instances with up to 40 targets and demonstrate its smaller median runtime than a baseline based on prior work.

In deep metric learning, the triplet loss has emerged as a popular method to learn many computer vision and natural language processing tasks such as facial recognition, object detection, and visual-semantic embeddings. One issue that plagues the triplet loss is network collapse, an undesirable phenomenon where the network projects the embeddings of all data onto a single point. Researchers predominately solve this problem by using triplet mining strategies. While hard negative mining is the most effective of these strategies, existing formulations lack strong theoretical justification for their empirical success. In this paper, we utilize the mathematical theory of isometric approximation to show an equivalence between the triplet loss sampled by hard negative mining and an optimization problem that minimizes a Hausdorff-like distance between the neural network and its ideal counterpart function. This provides the theoretical justifications for hard negative mining's empirical efficacy. Experiments performed on the Market-1501 and Stanford Online Products datasets with various network architectures corroborate our theoretical findings, indicating that network collapse tends to happen when batch size is too large or embedding dimension is too small. In addition, our novel application of the isometric approximation theorem provides the groundwork for future forms of hard negative mining that avoid network collapse.

We develop a planner that directs robots to construct a 3D target structure composed of blocks. The robots themselves are cubes of the same size as the blocks, and they may place, carry, or remove one block at a time. When moving, robots are also allowed to climb or descend a block. A construction plan may thus build a staircase-like scaffolding of blocks to reach other blocks at higher levels. The order of block placement is important; for example, a block that sits atop other blocks must be placed after the blocks below it, and a block that needs scaffolding cannot be placed until after the scaffolding is. Prior works focus on end-to-end approaches that simultaneously plan for block placement order and inter-robot collisions. Larger structures are either intractable or yield high-cost solutions. A prior approach mitigates this by decomposing the structure into smaller components that can be planned for independently, but the computational challenge remains. We present a hierarchical approach that first 1) uses A* to determine a sequence of block placements and removals while ignoring inter-robot collision, then 2) identifies ordering constraints between block placement and removal actions, and finally (3) computes collision-free paths for multiple robots to perform said actions. Compared to an optimization approach that minimizes the number of timesteps to complete the structure, we observe a 100x reduction in computation time for comparable solutions.

In this paper, we present a novel motion planning algorithm that inherits the strengths of both optimization and search-based planners. Optimization-based planners use the gradient of an objective function to generate a desired path, whereas search-based planners operate on a graph capturing the salient topology of a robot’s free space. A class of optimization-based planners leverages prior information, modeled as a probability distribution of target locations in an environment, to guide path generation. We embrace one specific measure, referred to as ergodicity, which encourages a robot to spend a proportion of its time, weighted by the distribution, where it is likely to find targets of interest. Methods that minimize ergodicity were not designed to handle obstacles in the environment, and augmented approaches that add "soft" constraints for obstacles to the cost function may still yield a path that collides with an obstacle. In this work, we present a hybrid approach that first generates a graph of the environment’s free space, followed by searching the graph with ergodicity as a heuristic. Our approach not only restricts the search to the free space, thereby avoiding obstacles by design, but also generates trajectories with low ergodicity values. Extensive testing on 125 test scenarios with varying degrees of clutter, information distribution, and robot start locations illustrate the efficacy of our algorithm.

Robotic systems need advanced mobility capabili-ties to operate in complex, three-dimensional environments designed for human use, e.g., multi-level buildings. Incorporating some level of autonomy enables robots to operate robustly, reliably, and efficiently in such complex environments, e.g., automatically “returning home” if communication between an operator and robot is lost during deployment. This work presents a novel method that enables mobile robots to robustly operate in multi-level environments by making it possible to autonomously locate and climb a range of different staircases. We present results wherein a wheeled robot works together with a quadrupedal system to quickly detect different staircases and reliably climb them. The performance of this novel staircase detection algorithm that is able to run on the heterogeneous platforms is compared to the current state-of-the-art detection algorithm. We show that our approach significantly increases the accuracy and speed at which detections occur.

Search and rescue applications often need multiple agents to complete a set of conflicting tasks. This paper studies a Multi-Agent Multi-Objective Ergodic Search (MA-MO-ES) approach to this problem where each objective or task is to cover a domain subject to an information map. The goal is to allocate coverage tasks to agents so that all maps are explored ergodically. The combinatorial nature of task allocation makes it computationally expensive to solve for optimal allocation using brute force. Apart from a large number of possible allocations, computing the cost of a task allocation is itself an expensive planning problem. To mitigate the computational challenge, we present a branch and bound-based algorithm with pruning techniques that reduce the number of allocations to be searched to find optimal coverage task allocation. We also present an approach to leverage the similarity between information maps to further reduce computation. Extensive testing on 147 randomly generated test cases shows an order of magnitude improvement in runtime compared to an exhaustive brute force approach.

Consider a Multi-Agent Collective Construction (MACC) problem that aims to generate a plan for fictitious cubic robots to build a three-dimensional structure comprised of cubic blocks. These cubic robots can carry one cubic block at a time; robots may move left, right, forwards, backward, or climb up or down one block. To construct structures taller than one cube, the robots must build supporting scaffolding made of blocks and remove the scaffolding once the structure is built. Prior works sought to create a planner that considered the structure as one monolithic assembly, which becomes intractable for larger workspaces and complex structures. To this end, we present a decomposition algorithm that breaks the structure into substructures that can be planned for independently. We use Mixed Integer Linear Programming (MILP) to plan for each of these substructures and then aggregate the solutions to construct the entire structure. Extensive testing on 200 randomly generated structures shows an order of magnitude improvement in the solution computation time compared to an MILP approach without decomposition. Finally, we leverage the independence between substructures to detect which substructures can be built in parallel.

Our work is motivated by humanitarian assistant and disaster relief (HADR) where often it is critical to find signs of life in the presence of conflicting criteria, objectives, and information. We believe ergodic search can provide a framework for exploiting available information as well as exploring for new information in applications, such as HADR. Existing ergodic search methods typically consider search using only a single information map. However, one can readily envision many scenarios where multiple information maps that encode different types of relevant information are used. Ergodic search methods currently do not possess the ability to simultaneously search multiple information maps, nor do they have a way to balance which information gets priority. This leads us to formulate a multiobjective ergodic search (MO-ES) problem, which aims to find the so-called Pareto-optimal solutions, for the purpose of providing human decision makers various solutions that trade off among conflicting criteria. To efficiently solve MO-ES, we develop a framework called sequential local ergodic search (SL-ES), which leverages the recent advances in ergodic search methods as well as the idea of local optimization to efficiently compute Pareto-optimal solutions. Our numerical results show that SL-ES computes solutions of better quality and runs faster than the baselines.

Safety considerations call for deployment of autonomous ground vehicles in defense and high risk zones for transport of goods from one point to another. Such vehicles face the threat of an intelligent autonomous adversary that may disrupt the transfer of material. This article investigates the challenges involved in autonomous protection of a delivery agent, via a land-based rescue agent, before interception of the delivery agent by the adversary occurs. In particular, we study how effectively an adversary equipped with a vision sensor can be handled by an autonomous rescue agent operating without vision support and relying only on wireless communication with the delivery agent. Taking capabilities and weights of the three vehicles into account, the delivery agent is assumed to be the slowest while the adversary operates at the highest speed among the three vehicles. A geometric framework based on Apollonius circles is proposed to analyze the interaction between the delivery and rescue agents. The adversary's speed and its moves (based on the direction of the delivery agent) are taken into account, along with the Apollonius circles for the rescue-delivery agent pair, to determine the possibility of capture. Regions in the plane where the delivery and rescue agents can meet, prior to a capture by the adversary, are obtained to compute safe regions for the delivery agent. Algorithms adopted by the delivery agent, rescue agent, and the adversary are described. We, then, explore the challenges in rescue of multiple delivery agents from a vision-guided adversary by introducing additional rescue agents. In particular, we study protection of k delivery agents (from an adversary) via k rescue agents. Algorithms to compute 1) multiple meeting points, one each for a delivery agent-rescue agent pair and 2) the strategy of the adversary to capture any one of the k delivery agents are presented. Experiments with multiple agents show that the delivery and rescue agents can execute their strategies using simply low-end microcontrollers without external memory.

Multiple autonomous agents working cooperatively have contributed to the development of robust large-scale systems. While substantial work has been done in manufacturing and domestic environments, a key consideration for small hardware agents engaged in collaborative factory automation and welfare support systems is limited area and power on-board. When the agents attempt to meet for performing a task, it is natural for them to encounter obstacles and it is desirable for each agent to optimize its resources during its navigation. In this paper, we develop efficient geometric algorithms to find a point, termed as the gathering point (and denoted by PG), for the agents that minimizes the maximum of path lengths. In particular, we present an O(n log2n) time algorithm for calculation of PGfor an environment with two agents and n static polygonal obstacles. We then use the notion of a weighted minimax point to derive an efficient algorithm (with complexity of O(k2+ kn log2n)) for computing PGfor an environment with k agents and n obstacles. An enhancement to a dynamic environment is then presented. We also present details of an efficient hardware realization of the algorithms. Each agent, equipped with only an ATmega328P microcontroller and no external memory, executes the algorithms. Experiments with multiple agents navigating amidst static as well as dynamic obstacles are reported.

Rendezvous of multiple autonomous agents has been of active interest in the last decade. Considerable work has been done on this problem with constraints on sensing and shape of the environment. However, not much is known on rendezvous amidst obstacles. When obstacles are introduced into the setting, it becomes natural to explore strategies for rendezvous that optimize some parameter (such as distance, time etc.). Our objective in this paper is to compute a location (which we refer to as the Time Optimal Rendezvous Point (TORP)) that minimizes the time for rendezvous amidst obstacles. We discuss challenges in finding TORP and develop efficient algorithms to compute TORP for r agents moving amidst m static polygonal obstacles. We then extend the analysis to handle dynamic obstacles. Experimental results are presented to validate the theory.