Glenn Wagner

M*: A complete multirobot path planning algorithm with performance bounds

Multirobot path planning is difficult because the full configuration space of the system grows exponentially with the number of robots. Planning in the joint configuration space of a set of robots is only necessary if they are strongly coupled, which is often not true if the robots are well separated in the workspace. Therefore, we initially plan for each robot separately, and only couple sets of robots after they have been found to interact, thus minimizing the dimensionality of the search space. We present a general strategy called subdimensional expansion, which dynamically generates low dimensional search spaces embedded in the full configuration space. We also present an implementation of subdimensional expansion for robot configuration spaces that can be represented as a graph, called M*, and show that M* is complete and finds minimal cost paths.

Subdimensional Expansion for Multirobot Path Planning

Abstract Planning optimal paths for large numbers of robots is computationally expensive. In this paper, we introduce a new framework for multirobot path planning called subdimensional expansion, which initially plans for each robot individually, and then coordinates motion among the robots as needed. More specifically, subdimensional expansion initially creates a one-dimensional search space embedded in the joint configuration space of the multirobot system. When the search space is found to be blocked during planning by a robot–robot collision, the dimensionality of the search space is locally increased to ensure that an alternative path can be found. As a result, robots are only coordinated when necessary, which reduces the computational cost of finding a path. We present the M ⁎ algorithm, an implementation of subdimensional expansion that adapts the A ⁎ planner to perform efficient multirobot planning. M ⁎ is proven to be complete and to find minimal cost paths. Simulation results are presented that show that M ⁎ outperforms existing optimal multirobot path planning algorithms.

Probabilistic path planning for multiple robots with subdimensional expansion

Probabilistic planners such as Rapidly-Exploring Random Trees (RRTs) and Probabilistic Roadmaps (PRMs) are powerful path planning algorithms for high dimensional systems, but even these potent techniques suffer from the curse of dimensionality, as can be seen in multirobot systems. In this paper, we apply a technique called subdimensional expansion in order to enhance the performance of probabilistic planners for multirobot path planning.We accomplish this by exploiting the structure inherent to such problems. Subdimensional expansion initially plans in each individual robots configuration space separately. It then couples those spaces when robots come into close proximity with one another. In this way, we constrain a probabilistic planner to search a low dimensional space, while dynamically generating a higher dimensional space where necessary. We show in simulation that subdimensional expansion enhanced PRMs can solve problems involving 32 robots and 128 total degrees of freedom in less than 10 minutes. We also demonstrate that enhancing RRTs and PRMs with subdimensional expansion can decrease the time required to find a solution by more than an order of magnitude.

ODrM* optimal multirobot path planning in low dimensional search spaces

We believe the core of handling the complexity of coordinated multiagent search lies in identifying which subsets of robots can be safely decoupled, and hence planned for in a lower dimensional space. Our work, as well as those of others take that perspective. In our prior work, we introduced an approach called subdimensional expansion for constructing low-dimensional but sufficient search spaces for multirobot path planning, and an implementation for graph search called M*. Subdimensional expansion dynamically increases the dimensionality of the search space in regions featuring significant robot-robot interactions. In this paper, we integrate M* with Meta-Agent Constraint-Based Search (MA-CBS), a planning framework that seeks to couple repeatedly colliding robots allowing for other robots to be planned in low-dimensional search space. M* is also integrated with operator decomposition (OD), an A*-variant performing lazy search of the outneighbors of a given vertex. We show that the combined algorithm demonstrates state of the art performance.

Gaussian reconstruction of swarm behavior from partial data

Swarms consist of large numbers of individual agents that generally maintain no fixed relative positions, which makes describing the behavior of the swarm as a whole difficult. Furthermore, the high number of agents leads to frequent occlusions that prevent observations of the entire swarm. In this paper, we represent the behavior of swarms using velocity fields, yielding a description which is invariant to the number of agents in a swarm, and the position, orientation, and scale of the swarm. The velocity field representation allows the behavior of swarms to be modeled as a Gaussian distribution. We demonstrate that this Gaussian model can be used to reconstruct the behavior of the swarm as a whole from partial observations.

Constraint Manifold Subsearch for multirobot path planning with cooperative tasks

The cooperative path planning problem seeks to determine a path for a group of robots which form temporary teams to perform tasks that require multiple robots. The multi-scale effects of simultaneously coordinating many robots distributed across the workspace while also tightly coordinating robots in cooperative teams increases the difficulty of planning. This paper describes a new approach to cooperative path planning called Constraint Manifold Subsearch (CMS). CMS builds upon M*, a high performance multirobot path planning algorithm, by modifying the search space to restrict teams of robots performing a task to the constraint manifold of the task. CMS can find optimal solutions to the cooperative path planning problem, or near optimal solutions to problems involving large numbers of robots.

Multirobot sequential composition

Conventional path planning algorithms compute a single path through the configuration space. There is no guarantee that a physical robot will be able to track the trajectory while avoiding collisions, particularly in the presence of environmental perturbations and errors in the process model. Sequential composition combines planning and control by computing a sequence of controllers to execute rather than a single trajectory, offering greater safety guarantees. In this paper, we apply sequential composition to multirobot systems in a scalable fashion using M*, an advanced multirobot path planning algorithm. Controllers will vary in size and geometry, and thus take different amounts of time to execute. To handle these differences, we introduce the time augmented joint prepares graph and the approximate time augmented joint prepares graph which simplifies implementation by discretizing time. We validate our approach in a mixed reality test framework.

M*: A Complete Multirobot Path Planning Algorithm with Optimality Bounds

Multirobot path planning is difficult because the full configuration space of the system grows exponentially with the number of robots. Planning in the joint configuration space of a set of robots is only necessary if they are strongly coupled, which is often not true if the robots are well separated in the workspace. Therefore, we initially plan for each robot separately, and only couple sets of robots after they have been found to interact, thus minimizing the dimensionality of the search space. We present a general strategy called subdimensional expansion, which dynamically generates low dimensional search spaces embedded in the full configuration space. We also present an implementation of subdimensional expansion for robot configuration spaces that can be represented as a graph, called M*, and show that M* is complete and finds minimal cost paths.