Nicholas M. Stiffler

Shortest paths for visibility-based pursuit-evasion

We present an algorithm that computes a minimal-cost pursuer trajectory for a single pursuer to solve the visibility-based pursuit-evasion problem in a simply-connected two-dimensional environment. This algorithm improves upon the known algorithm of Guibas, Latombe, LaValle, Lin, and Motwani, which is complete but not optimal. Our algorithm uses a Tour of Segments (ToS) subroutine to construct a pursuer path that minimizes the distance traveled by the pursuer while guaranteeing that all evaders in the environment will be captured. We have implemented our algorithm in simulation and provide results.

Pursuit-evasion with fixed beams

We introduce a complete algorithm for solving a pursuit-evasion problem in a simply-connected two-dimensional environment, for the case of a single pursuer equipped with fixed beam sensors. The input for our algorithm is an environment and a collection of sensor directions, in which each is capable of line-of-sight detection in a fixed direction. The output is a pursuer motion strategy that ensures the detection of an evader that moves with unbounded speed, or a statement that no such strategy exists. The intuition of the algorithmis to decompose the environment into a collection of convex conservative regions, within which the evader cannot sneak between any pair of adjacent sensors. This decomposition induces a graph we call the pursuit-evasion graph (PEG), such that any correct solution strategy can be expressed as a path through the PEG. For an instance defined by m beams and an environment with n vertices, the algorithm runs in time O(2mn2). We implemented the algorithm in simulation and present some computed examples illustrating the algorithms correctness.

Visibility-based pursuit-evasion with probabilistic evader models

We propose an algorithm for a visibility-based pursuit-evasion problem in a simply-connected two-dimensional environment, in which a single pursuer has access to a probabilistic model describing how the evaders are likely to move in the environment. The application of our algorithm can be best viewed in the context of search and rescue: Although the victims (evaders) are not actively trying to escape from the robot, it is necessary to consider the task of locating the victims as a pursuit-evasion problem to obtain a firm guarantee that all of the victims are found. We present an algorithm that draws sample evader trajectories from the probabilistic model to compute a plan that lowers the Expected Time to Capture the evaders without drastically increasing the Guaranteed Time to Capture the evaders. We introduce a graph structure that takes advantage of the sampled evader trajectories to compute a path that would “see” all the evaders if they followed only those trajectories in our sampled set. We then use a previous technique to append our path with actions that provide a complete solution for the visibility-based pursuit-evasion problem. The resulting plan guarantees that all evaders are located, even if they do not obey the given probabilistic motion model. We implemented the algorithm in a simulation and provide a quantitative comparison to existing methods.

High-Quality Tabletop Rearrangement with Overhand Grasps: Hardness Results and Fast Methods

This paper studies the underlying combinatorial structure of a class of object rearrangement problems, which appear frequently in applications. The problems involve multiple, similar-geometry objects placed on a flat, horizontal surface, where a robot can approach them from above and perform pick-and-place operations to rearrange them. The paper considers both the case where the start and goal object poses overlap, and where they do not. For overlapping poses, the primary objective is to minimize the number of pick-and-place actions and then to minimize the distance traveled by the end-effector. For the non-overlapping case, the objective is solely to minimize the end-effector distance. While such problems do not involve all the complexities of general rearrangement, they remain computationally hard challenges in both cases. This is shown through two-way reductions between well-understood, hard combinatorial challenges and these rearrangement problems. The benefit of the reduction is that there are well studied algorithms for solving these well-established combinatorial challenges. These algorithms can be very efficient in practice despite the hardness results. The paper builds on these reduction results to propose an algorithmic pipeline for dealing with the rearrangement problems. Experimental evaluation shows that the proposed pipeline achieves high-quality paths with regards to the optimization objectives. Furthermore, it exhibits highly desirable scalability as the number of objects increases in both the overlapping and non-overlapping setups.

Complete and optimal visibility-based pursuit-evasion

This paper computes a minimum-length pursuer trajectory that solves a visibility-based pursuit-evasion problem in which a single pursuer moving through a simply-connected polygonal environment seeks to locate an evader which may move arbitrarily fast, using an omni-directional field-of-view that extends to the environment boundary. We present a complete algorithm that computes a minimum-cost pursuer trajectory that ensures that the evader is captured, or reports in finite time that no such trajectory exists. This result improves upon the known algorithm of Guibas, Latombe, LaValle, Lin, and Motwani, which is complete but makes no guarantees about the quality of the solution. Our algorithm employs a branch-and-bound forward search that considers pursuer trajectories that could potentially lead to an optimal pursuer strategy. The search is performed on an exponential graph that can generate an infinite number of unique pursuer trajectories, so we must conduct meticulous pruning during the search to quickly discard pursuer trajectories that are demonstrably suboptimal. We describe an implementation of the algorithm, along with experiments that measure its performance in several environments with a variety of pruning operations.

Complexity Results and Fast Methods for Optimal Tabletop Rearrangement with Overhand Grasps

This paper studies the underlying combinatorial structure of a class of object rearrangement problems, which appear frequently in applications. The problems involve multiple, similar-geometry objects placed on a flat, horizontal surface, where a robot can approach them from above and perform pick-and-place operations to rearrange them. The paper considers both the case where the start and goal object poses overlap, and where they do not. For overlapping poses, the primary objective is to minimize the number of pick-and-place actions and then to minimize the distance traveled by the end-effector. For the non-overlapping case, the objective is solely to minimize the travel distance of the end-effector. Although such problems do not involve all the complexities of general rearrangement, they remain computationally hard in both cases. This is shown through reductions from well-understood, hard combinatorial challenges to these rearrangement problems. The reductions are also shown to hold in the reverse direction, which enables the convenient application on rearrangement of well-studied algorithms. These algorithms can be very efficient in practice despite the hardness results. The paper builds on these reduction results to propose an algorithmic pipeline for dealing with the rearrangement problems. Experimental evaluation, including hardware-based trials, shows that the proposed pipeline computes high-quality paths with regards to the optimization objectives. Furthermore, it exhibits highly desirable scalability as the number of objects increases in both the overlapping and non-overlapping setup.

Persistent pursuit-evasion: The case of the preoccupied pursuer

We consider a visibility-based pursuit-evasion problem in which a single robot with an omnidirectional but unreliable sensor moving through an environment must systematically search that environment to detect an unpredictably moving target. A common assumption in visibility-based pursuit-evasion is that the sensors used to detect the evader are perfectly reliable. That is, any evader that moves within view of the pursuer for any interval of time will be detected. This assumption is problematic because, when implemented on real sensor systems, such plans cannot account for the possibility of short-term false negative errors in evader detection. This paper addresses this limitation by introducing a model based on the idea of pessimal unoccluded distance to reason about the degree of plausibility that the evader may be concealed within each occluded region. We describe a decomposition of the environment that fully characterizes the opportune moment for an evader to take advantage of sensor error. Furthermore, we present a complete algorithm that solves the active problem of planning a search for a pursuer which maximizes the distance that the evader must travel through the pursuer robots sensor footprint.

Agent classification using implicit models

We present an algorithm that uses a sparse collection of noisy sensors to characterize the observed behavior of a mobile agent. Our approach models the agents behavior using a collection of randomized simulators called implicit agent models and seeks to classify the agent according to which of these models is believed to be governing its motions. To accomplish this, we introduce an algorithm whose input is an observation sequence generated by the agent, represented as sensor label-time pairs, along with an observation sequence generated by one of our implicit agent models and whose output is a measure of the similarity between the two observation sequences. Using this similarity measure, we propose two algorithms for the model classification problem: one based on a weighted voting scheme and one that uses intermediate resampling steps. We have implemented these algorithms in simulation, and present results demonstrating their effectiveness in correctly classifying mobile agents.