arXiv subjects

Zhongqiang Ren

Publications and source records attributed to Zhongqiang Ren.

At least 37 records · Page 2Linked to original sources

arXiv2025

A Mixed-Integer Conic Program for the Moving-Target Traveling Salesman Problem based on a Graph of Convex Sets

This paper introduces a new formulation that finds the optimum for the Moving-Target Traveling Salesman Problem (MT-TSP), which seeks to find a shortest path for an agent, that starts at a depot, visits a set of moving targets exactly once within their assigned time-windows, and returns to the depot. The formulation relies on the key idea that when the targets move along lines, their trajectories become convex sets within the space-time coordinate system. The problem then reduces to finding the shortest path within a graph of convex sets, subject to some speed constraints. We compare our formulation with the current state-of-the-art Mixed Integer Conic Program (MICP) solver for the MT-TSP. The experimental results show that our formulation outperforms the MICP for instances with up to 20 targets, with up to two orders of magnitude reduction in runtime, and up to a 60\% tighter optimality gap. We also show that the solution cost from the convex relaxation of our formulation provides significantly tighter lower bounds for the MT-TSP than the ones from the MICP.

cs.RO↗

arXiv2024

Loosely Synchronized Rule-Based Planning for Multi-Agent Path Finding with Asynchronous Actions

Multi-Agent Path Finding (MAPF) seeks collision-free paths for multiple agents from their respective starting locations to their respective goal locations while minimizing path costs. Although many MAPF algorithms were developed and can handle up to thousands of agents, they usually rely on the assumption that each action of the agent takes a time unit, and the actions of all agents are synchronized in a sense that the actions of agents start at the same discrete time step, which may limit their use in practice. Only a few algorithms were developed to address asynchronous actions, and they all lie on one end of the spectrum, focusing on finding optimal solutions with limited scalability. This paper develops new planners that lie on the other end of the spectrum, trading off solution quality for scalability, by finding an unbounded sub-optimal solution for many agents. Our method leverages both search methods (LSS) in handling asynchronous actions and rule-based planning methods (PIBT) for MAPF. We analyze the properties of our method and test it against several baselines with up to 1000 agents in various maps. Given a runtime limit, our method can handle an order of magnitude more agents than the baselines with about 25% longer makespan.

cs.MA↗

arXiv2024

C*: A New Bounding Approach for the Moving-Target Traveling Salesman Problem

We introduce a new bounding approach called Continuity* C*, which provides optimality guarantees for the Moving-Target Traveling Salesman Problem (MT-TSP). Our approach relaxes the continuity constraints on the agent's tour by partitioning the targets' trajectories into smaller segments. This allows the agent to arrive at any point within a segment and depart from any point in the same segment when visiting each target. This formulation enables us to pose the bounding problem as a Generalized Traveling Salesman Problem (GTSP) on a graph, where the cost of traveling along an edge requires solving a new problem called the Shortest Feasible Travel (SFT). We present various methods for computing bounds for the SFT problem, leading to several variants of C*. We first prove that the proposed algorithms provide valid lower-bounds for the MT-TSP. Additionally, we provide computational results to validate the performance of all C* variants on instances with up to 15 targets. For the special case where targets move along straight lines, we compare our C* variants with a mixed-integer Second Order Conic Program (SOCP) based method, the current state-of-the-art solver for the MT-TSP. While the SOCP-based method performs well on instances with 5 and 10 targets, C* outperforms it on instances with 15 targets. For the general case, on average, our approaches find feasible solutions within approximately 4.5% of the lower-bounds for the tested instances.

cs.RO↗

arXiv2024

A Complete Algorithm for a Moving Target Traveling Salesman Problem with Obstacles

The moving target traveling salesman problem with obstacles (MT-TSP-O) is a generalization of the traveling salesman problem (TSP) where, as its name suggests, the targets are moving. A solution to the MT-TSP-O is a trajectory that visits each moving target during a certain time window(s), and this trajectory avoids stationary obstacles. We assume each target moves at a constant velocity during each of its time windows. The agent has a speed limit, and this speed limit is no smaller than any target's speed. This paper presents the first complete algorithm for finding feasible solutions to the MT-TSP-O. Our algorithm builds a tree where the nodes are agent trajectories intercepting a unique sequence of targets within a unique sequence of time windows. We generate each of a parent node's children by extending the parent's trajectory to intercept one additional target, each child corresponding to a different choice of target and time window. This extension consists of planning a trajectory from the parent trajectory's final point in space-time to a moving target. To solve this point-to-moving-target subproblem, we define a novel generalization of a visibility graph called a moving target visibility graph (MTVG). Our overall algorithm is called MTVG-TSP. To validate MTVG-TSP, we test it on 570 instances with up to 30 targets. We implement a baseline method that samples trajectories of targets into points, based on prior work on special cases of the MT-TSP-O. MTVG-TSP finds feasible solutions in all cases where the baseline does, and when the sum of the targets' time window lengths enters a critical range, MTVG-TSP finds a feasible solution with up to 38 times less computation time.

cs.RO↗

arXiv2024

Multi-Agent Combinatorial Path Finding with Heterogeneous Task Duration

Multi-Agent Combinatorial Path Finding (MCPF) seeks collision-free paths for multiple agents from their initial locations to destinations, visiting a set of intermediate target locations in the middle of the paths, while minimizing the sum of arrival times. While a few approaches have been developed to handle MCPF, most of them simply direct the agent to visit the targets without considering the task duration, i.e., the amount of time needed for an agent to execute the task (such as picking an item) at a target location. MCPF is NP-hard to solve to optimality, and the inclusion of task duration further complicates the problem. This paper investigates heterogeneous task duration, where the duration can be different with respect to both the agents and targets. We develop two methods, where the first method post-processes the paths planned by any MCPF planner to include the task duration and has no solution optimality guarantee; and the second method considers task duration during planning and is able to ensure solution optimality. The numerical and simulation results show that our methods can handle up to 20 agents and 50 targets in the presence of task duration, and can execute the paths subject to robot motion disturbance.

cs.RO↗

arXiv2024

iMTSP: Solving Min-Max Multiple Traveling Salesman Problem with Imperative Learning

This paper considers a Min-Max Multiple Traveling Salesman Problem (MTSP), where the goal is to find a set of tours, one for each agent, to collectively visit all the cities while minimizing the length of the longest tour. Though MTSP has been widely studied, obtaining near-optimal solutions for large-scale problems is still challenging due to its NP-hardness. Recent efforts in data-driven methods face challenges of the need for hard-to-obtain supervision and issues with high variance in gradient estimations, leading to slow convergence and highly suboptimal solutions. We address these issues by reformulating MTSP as a bilevel optimization problem, using the concept of imperative learning (IL). This involves introducing an allocation network that decomposes the MTSP into multiple single-agent traveling salesman problems (TSPs). The longest tour from these TSP solutions is then used to self-supervise the allocation network, resulting in a new self-supervised, bilevel, end-to-end learning framework, which we refer to as imperative MTSP (iMTSP). Additionally, to tackle the high-variance gradient issues during the optimization, we introduce a control variate-based gradient estimation algorithm. Our experiments showed that these innovative designs enable our gradient estimator to converge 20% faster than the advanced reinforcement learning baseline and find up to 80% shorter tour length compared with Google OR-Tools MTSP solver, especially in large-scale problems (e.g. 1000 cities and 15 agents).

cs.AI↗

arXiv2024

PWTO: A Heuristic Approach for Trajectory Optimization in Complex Terrains

This paper considers a trajectory planning problem for a robot navigating complex terrains, which arises in applications ranging from autonomous mining vehicles to planetary rovers. The problem seeks to find a low-cost dynamically feasible trajectory for the robot. The problem is challenging as it requires solving a non-linear optimization problem that often has many local minima due to the complex terrain. To address the challenge, we propose a method called Pareto-optimal Warm-started Trajectory Optimization (PWTO) that attempts to combine the benefits of graph search and trajectory optimization, two very different approaches to planning. PWTO first creates a state lattice using simplified dynamics of the robot and leverages a multi-objective graph search method to obtain a set of paths. Each of the paths is then used to warm-start a local trajectory optimization process, so that different local minima are explored to find a globally low-cost solution. In our tests, the solution cost computed by PWTO is often less than half of the costs computed by the baselines. In addition, we verify the trajectories generated by PWTO in Gazebo simulation in complex terrains with both wheeled and quadruped robots. The code of this paper is open sourced and can be found at https://github.com/rap-lab-org/public_pwto.

cs.RO↗

arXiv2024

Propagative Distance Optimization for Constrained Inverse Kinematics

This paper investigates a constrained inverse kinematic (IK) problem that seeks a feasible configuration of an articulated robot under various constraints such as joint limits and obstacle collision avoidance. Due to the high-dimensionality and complex constraints, this problem is often solved numerically via iterative local optimization. Classic local optimization methods take joint angles as the decision variable, which suffers from non-linearity caused by the trigonometric constraints. Recently, distance-based IK methods have been developed as an alternative approach that formulates IK as an optimization over the distances among points attached to the robot and the obstacles. Although distance-based methods have demonstrated unique advantages, they still suffer from low computational efficiency, since these approaches usually ignore the chain structure in the kinematics of serial robots. This paper proposes a new method called propagative distance optimization for constrained inverse kinematics (PDO-IK), which captures and leverages the chain structure in the distance-based formulation and expedites the optimization by computing forward kinematics and the Jacobian propagatively along the kinematic chain. Test results show that PDO-IK runs up to two orders of magnitude faster than the existing distance-based methods under joint limits constraints and obstacle avoidance constraints. It also achieves up to three times higher success rates than the conventional joint-angle-based optimization methods for IK problems. The high runtime efficiency of PDO-IK allows the real-time computation (10$-$1500 Hz) and enables a simulated humanoid robot with 19 degrees of freedom (DoFs) to avoid moving obstacles, which is otherwise hard to achieve with the baselines.

cs.RO↗

arXiv2024

DMS*: Minimizing Makespan for Multi-Agent Combinatorial Path Finding

Multi-Agent Combinatorial Path Finding (MCPF) seeks collision-free paths for multiple agents from their initial to goal locations, while visiting a set of intermediate target locations in the middle of the paths. MCPF is challenging as it involves both planning collision-free paths for multiple agents and target sequencing, i.e., solving traveling salesman problems to assign targets to and find the visiting order for the agents. Recent work develops methods to address MCPF while minimizing the sum of individual arrival times at goals. Such a problem formulation may result in paths with different arrival times and lead to a long makespan, the maximum arrival time, among the agents. This paper proposes a min-max variant of MCPF, denoted as MCPF-max, that minimizes the makespan of the agents. While the existing methods (such as MS*) for MCPF can be adapted to solve MCPF-max, we further develop two new techniques based on MS* to defer the expensive target sequencing during planning to expedite the overall computation. We analyze the properties of the resulting algorithm Deferred MS* (DMS*), and test DMS* with up to 20 agents and 80 targets. We demonstrate the use of DMS* on differential-drive robots.

cs.RO↗

arXiv2023

Solving Multi-Agent Target Assignment and Path Finding with a Single Constraint Tree

Combined Target-Assignment and Path-Finding problem (TAPF) requires simultaneously assigning targets to agents and planning collision-free paths for agents from their start locations to their assigned targets. As a leading approach to address TAPF, Conflict-Based Search with Target Assignment (CBS-TA) leverages both K-best target assignments to create multiple search trees and Conflict-Based Search (CBS) to resolve collisions in each search tree. While being able to find an optimal solution, CBS-TA suffers from scalability due to the duplicated collision resolution in multiple trees and the expensive computation of K-best assignments. We therefore develop Incremental Target Assignment CBS (ITA-CBS) to bypass these two computational bottlenecks. ITA-CBS generates only a single search tree and avoids computing K-best assignments by incrementally computing new 1-best assignments during the search. We show that, in theory, ITA-CBS is guaranteed to find an optimal solution and, in practice, is computationally efficient.

cs.AI↗

arXiv2023

Enhanced Multi-Objective A* with Partial Expansion

The Multi-Objective Shortest Path Problem (MO-SPP), typically posed on a graph, determines a set of paths from a start vertex to a destination vertex while optimizing multiple objectives. In general, there does not exist a single solution path that can simultaneously optimize all the objectives and the problem thus seeks to find a set of so-called Pareto-optimal solutions. To address this problem, several Multi-Objective A* (MOA*) algorithms were recently developed to quickly compute solutions with quality guarantees. However, these MOA* algorithms often suffer from high memory usage, especially when the branching factor (i.e. the number of neighbors of any vertex) of the graph is large. This work thus aims at reducing the high memory consumption of MOA* with little increase in the runtime. By generalizing and unifying several single- and multi-objective search algorithms, we develop the Runtime and Memory Efficient MOA* (RME-MOA*) approach, which can balance between runtime and memory efficiency by tuning two user-defined hyper-parameters.

math.OC↗

arXiv2023

PyPose: A Library for Robot Learning with Physics-based Optimization

Deep learning has had remarkable success in robotic perception, but its data-centric nature suffers when it comes to generalizing to ever-changing environments. By contrast, physics-based optimization generalizes better, but it does not perform as well in complicated tasks due to the lack of high-level semantic information and reliance on manual parametric tuning. To take advantage of these two complementary worlds, we present PyPose: a robotics-oriented, PyTorch-based library that combines deep perceptual models with physics-based optimization. PyPose's architecture is tidy and well-organized, it has an imperative style interface and is efficient and user-friendly, making it easy to integrate into real-world robotic applications. Besides, it supports parallel computing of any order gradients of Lie groups and Lie algebras and $2^{\text{nd}}$-order optimizers, such as trust region methods. Experiments show that PyPose achieves more than $10\times$ speedup in computation compared to the state-of-the-art libraries. To boost future research, we provide concrete examples for several fields of robot learning, including SLAM, planning, control, and inertial navigation.

cs.RO↗

arXiv2022

MUI-TARE: Multi-Agent Cooperative Exploration with Unknown Initial Position

Multi-agent exploration of a bounded 3D environment with unknown initial positions of agents is a challenging problem. It requires quickly exploring the environments as well as robustly merging the sub-maps built by the agents. We take the view that the existing approaches are either aggressive or conservative: Aggressive strategies merge two sub-maps built by different agents together when overlap is detected, which can lead to incorrect merging due to the false-positive detection of the overlap and is thus not robust. Conservative strategies direct one agent to revisit an excessive amount of the historical trajectory of another agent for verification before merging, which can lower the exploration efficiency due to the repeated exploration of the same space. To intelligently balance the robustness of sub-map merging and exploration efficiency, we develop a new approach for lidar-based multi-agent exploration, which can direct one agent to repeat another agent's trajectory in an \emph{adaptive} manner based on the quality indicator of the sub-map merging process. Additionally, our approach extends the recent single-agent hierarchical exploration strategy to multiple agents in a \emph{cooperative} manner by planning for agents with merged sub-maps together to further improve exploration efficiency. Our experiments show that our approach is up to 50\% more efficient than the baselines on average while merging sub-maps robustly.

cs.RO↗

arXiv2022

A Local Optimization Framework for Multi-Objective Ergodic Search

Robots have the potential to perform search for a variety of applications under different scenarios. 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 for applications such as HADR, especially when time is of the essence. Ergodic search algorithms plan trajectories such that the time spent in a region is proportional to the amount of information in that region, and is able to naturally balance exploitation (myopically searching high-information areas) and exploration (visiting all locations in the search space for new information). Existing ergodic search algorithms, as well as other information-based approaches, typically consider search using only a single information map. However, in many scenarios, the use of multiple information maps that encode different types of relevant information is common. Ergodic search methods currently do not possess the ability for simultaneous nor do they have a way to balance which information gets priority. This leads us to formulate a Multi-Objective Ergodic Search (MOES) problem, which aims at finding the so-called Pareto-optimal solutions, for the purpose of providing human decision makers various solutions that trade off between conflicting criteria. To efficiently solve MOES, we develop a framework called Sequential Local Ergodic Search (SLES) that converts a MOES problem into a "weight space coverage" problem. It leverages the recent advances in ergodic search methods as well as the idea of local optimization to efficiently approximate the Pareto-optimal front. Our numerical results show that SLES runs distinctly faster than the baseline methods.

cs.RO↗

arXiv2022

A Conflict-Based Search Framework for Multi-Objective Multi-Agent Path Finding

Conventional multi-agent path planners typically compute an ensemble of paths while optimizing a single objective, such as path length. However, many applications may require multiple objectives, say fuel consumption and completion time, to be simultaneously optimized during planning and these criteria may not be readily compared and sometimes lie in competition with each other. The goal of the problem is thus to find a Pareto-optimal set of solutions instead of a single optimal solution. Naively applying existing multi-objective search algorithms, such as multi-objective A* (MOA*), to multi-agent path finding may prove to be inefficient as the dimensionality of the search space grows exponentially with the number of agents. This article presents an approach named Multi-Objective Conflict-Based Search (MO-CBS) that attempts to address this so-called curse of dimensionality by leveraging prior Conflict-Based Search (CBS), a well-known algorithm for single-objective multi-agent path finding, and principles of dominance from multi-objective optimization literature. We also develop several variants of MO-CBS to improve its performance. We prove that MO-CBS and its variants can compute the entire Pareto-optimal set. Numerical results show that MO-CBS outperforms MOM*, a recently developed state-of-the-art multi-objective multi-agent planner.

cs.AI↗

arXiv2022

A Lower Bounding Framework for Motion Planning amid Dynamic Obstacles in 2D

This work considers a Motion Planning Problem with Dynamic Obstacles (MPDO) in 2D that requires finding a minimum-arrival-time collision-free trajectory for a point robot between its start and goal locations amid dynamic obstacles moving along known trajectories. Existing methods, such as continuous Dijkstra paradigm, can find an optimal solution by restricting the shape of the obstacles or the motion of the robot, while this work makes no such assumptions. Other methods, such as search-based planners and sampling-based approaches can compute a feasible solution to this problem but do not provide approximation bounds. Since finding the optimum is challenging for MPDO, this paper develops a framework that can provide tight lower bounds to the optimum. These bounds act as proxies for the optimum which can then be used to bound the deviation of a feasible solution from the optimum. To accomplish this, we develop a framework that consists of (i) a bi-level discretization approach that converts the MPDO to a relaxed path planning problem, and (ii) an algorithm that can solve the relaxed problem to obtain lower bounds. We also present numerical results to corroborate the performance of the proposed framework. These results show that the bounds obtained by our approach for some instances are up to twice tighter than a baseline approach showcasing potential advantages of the proposed approach.

cs.RO↗

arXiv2022

Enhanced Multi-Objective A* Using Balanced Binary Search Trees

This work addresses a Multi-Objective Shortest Path Problem (MO-SPP) on a graph where the goal is to find a set of Pareto-optimal solutions from a start node to a destination in the graph. A family of approaches based on MOA* have been developed to solve MO-SPP in the literature. Typically, these approaches maintain a "frontier" set at each node during the search process to keep track of the non-dominated, partial paths to reach that node. This search process becomes computationally expensive when the number of objectives increases as the number of Pareto-optimal solutions becomes large. In this work, we introduce a new method to efficiently maintain these frontiers for multiple objectives by incrementally constructing balanced binary search trees within the MOA* search framework. We first show that our approach correctly finds the Pareto-optimal front, and then provide extensive simulation results for problems with three, four and five objectives to show that our method runs faster than existing techniques by up to an order of magnitude.

cs.AI↗

arXiv2022

Multi-objective Conflict-based Search Using Safe-interval Path Planning

This paper addresses a generalization of the well known multi-agent path finding (MAPF) problem that optimizes multiple conflicting objectives simultaneously such as travel time and path risk. This generalization, referred to as multi-objective MAPF (MOMAPF), arises in several applications ranging from hazardous material transportation to construction site planning. In this paper, we present a new multi-objective conflict-based search (MO-CBS) approach that relies on a novel multi-objective safe interval path planning (MO-SIPP) algorithm for its low-level search. We first develop the MO-SIPP algorithm, show its properties and then embed it in MO-CBS. We present extensive numerical results to show that (1) there is an order of magnitude improvement in the average low level search time, and (2) a significant improvement in the success rates of finding the Pareto-optimal front can be obtained using the proposed approach in comparison with the previous MO-CBS.

cs.RO↗