Ercan U. Acar

Path Planning for Robotic Demining: Robust Sensor-Based Coverage of Unstructured Environments and Probabilistic Methods

Demining and unexploded ordnance (UXO) clearance are extremely tedious and dangerous tasks. The use of robots bypasses the hazards and potentially increases the efficiency of both tasks. A first crucial step towards robotic mine/UXO clearance is to locate all the targets. This requires a path planner that generates a path to pass a detector over all points of a mine/UXO field, i.e., a planner that is complete.The current state of the art in path planning for mine/UXO clearance is to move a robot randomly or use simple heuristics. These methods do not possess completeness guarantees which are vital for locating all of the mines/UXOs. Using such random approaches is akin to intentionally using imperfect detectors. In this paper, we first overview our prior complete coverage algorithm and compare it with randomized approaches. In addition to the provable guarantees, we demonstrate that complete coverage achieves coverage in shorter time than random coverage. We also show that the use of complete approaches enables the creation of a filter to reject bad sensor readings, which is necessary for successful deployment of robots. We propose a new approach to handle sensor uncertainty that uses geometrical and topological features rather than sensor uncertainty models. We have verified our results by performing experiments in unstructured indoor environments. Finally, for scenarios where some a priori information about a minefield is available, we expedite the demining process by introducing a probabilistic method so that a demining robot does not have to perform exhaustive coverage.

Morse Decompositions for Coverage Tasks

Exact cellular decompositions represent a robots free space by dividing it into regions with simple structure such that the sum of the regions fills the free space. These decompositions have been widely used for path planning between two points, but can be used for mapping and coverage of free spaces. In this paper, we define exact cellular decompositions where critical points of Morse functions indicate the location of cell boundaries. Morse functions are those whose critical points are non-degenerate. Between critical points, the structure of a space is effectively the same, so simple control strategies to achieve tasks, such as coverage, are feasible within each cell. This allows us to introduce a general framework for coverage tasks because varying the Morse function has the effect of changing the pattern by which a robot covers its free space. In this paper, we give examples of different Morse functions and comment on their corresponding tasks. In a companion paper, we describe the sensor-based algorithm that constructs the decomposition.

Sensor-based Coverage of Unknown Environments: Incremental Construction of Morse Decompositions:

The goal of coverage path planning is to determine a path that passes a detector over all points in an environment. This work prescribes a provably complete coverage path planner for robots in unknown spaces. We achieve coverage using Morse decompositions which are exact cellular decompositions whose cells are defined in terms of critical points of Morse functions. Generically, two critical points define a cell. We encode the topology of the Morse decomposition using a graph that has nodes corresponding to the critical points and edges representing the cells defined by pairs of critical points. The robot simultaneously covers the space while incrementally constructing this graph. To achieve this, the robot must sense all the critical points. Therefore, we first introduce a critical point sensing method that uses range sensors. Then we present a provably complete algorithm which guarantees that the robot will encounter all the critical points, thereby constructing the full graph, i.e., achieving complete coverage. We also validate our approach by performing experiments on a mobile robot equipped with a sonar ring.

Exact cellular decomposition of closed orientable surfaces embedded in /spl Rfr//sup 3/

We address the task of covering a closed orientable surface embedded in /spl Rfr//sup 3/ without any prior information about the surface. For applications such as paint deposition, the effector (the paint atomizer) does not explicitly cover the target surface, but instead covers an offset surface-a surface that is a fixed distance away from the target surface. Just as Canny and others use critical points to look for changes in connectivity of the free space to ensure completeness of their roadmap algorithms, we use critical points to identify changes in the connectivity of the offset surface to ensure full surface coverage. The main contribution of this work is a method to construct unknown offset surfaces using a procedure, also developed in this paper, to detect critical points.

Sensor-based planning: exact cellular decompositions in terms of critical points

A coverage path planning algorithm produces a path that directs a robot (or its detector range, occupied volume, etc.) to sweep out a target volume. The goal of this work is to direct an agent to cover (fill) an unknown space using different coverage patterns. We achieve coverage by dividing the target region into sub-regions, termed cells, such that coverage in each cell can be accomplished by basic maneuvers, such as simple back-and-forth motions. This approach to coverage employs a representation of the free space called an exact cellular decomposition, which already has been widely used for path planning between two points. In this paper, we define exact cellular decompositions where critical points of Morse functions indicate the locations of cell boundaries. Morse functions are those whose critical points are non-degenerate. Different Morse functions induce different coverage patterns. Between critical points, the structure of a Morse function is effectively the same, so simple control laws to achieve tasks, such as coverage, are feasible within each cell. This paper addresses the issue of how to cover a space with varying patterns, but it also suggests a common framework for many conventional path planners. A companion paper describes the sensor based implementation of this approach.

Exploiting critical points to reduce positioning error for sensor-based navigation

This paper presents a planner that determines a path such that the robot does not have to heavily rely on odometry to reach its goal. The planner determines a sequence of obstacle boundaries that the robot must follow to reach the goal. Since this planner is used in the context of a coverage algorithm already presented by the authors, we assume that the free space is already, completely or partially, represented by a cellular decomposition whose cell boundaries are defined by critical points of Morse functions (isolated points at obstacle boundaries). The topological relationship among the cells is represented by a graph where nodes are the critical points and edges connect the nodes that define a common cell (i.e., the edges correspond to the cells themselves). A search of this graph yields a sequence of cells that directs the robot from a start to a goal. Once a sequence of cells and critical points are determined, a robot traverses each cell by mainly following the boundary of the cell along the obstacle boundaries and minimizes the accumulated dead-reckoning error at the intermediate critical points. This allows the robot to reach the goal robustly even in the presence of dead-reckoning error.

Sensor-Based Coverage: Incremental Construction of Cellular Decompositions

Coverage path planning determines a path that passes a robot, a detector, or some type of effector over all points in an environment. Previous work in coverage used cellular decompositions to pass a robot over all points in a target space. We defined a class of cellular decompositions termed Morse Decompositions which were defined by Morse functions; varying the Morse function changes the pattern by which the space was covered. In this paper, we prescribe a provably complete sensor-based coverage path planner that can accommodate detectors with variable effective detecting ranges that go beyond the robot’s periohery. In vast open spaces, the robot can use the full range of its detector, so we cover these spaces as if the robot were as big as the detector. In narrow and cluttered spaces, we obstacles lie within the detector range and thus the detection range “fills” the surrounding area; in this case, the robot simply follows the generalized Voronoi diagram in the cluttered spaces. Therefore, we introduce a new hierarchical decomposition that combines Morse decompositions and generalized Voronoi diagrams. We show how to use this hierarchical decomposition to cover unknown spaces.