Risk-aware graph search with dynamic edge cost discovery
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Jen Jen Chung↗
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Search Problems in Mission Planning and Navigation of Autonomous Aircraft
An architecture for the control of an autonomous aircraft is presented. The architecture is a hierarchical system representing an anthropomorphic breakdown of the control problem into planner, navigator, and pilot systems. The planner system determines high level global plans from overall mission objectives. This abstract mission planning is investigated by focusing on the Traveling Salesman Problem with variations on local and global constraints. Tree search techniques are applied including the breadth first, depth first, and best first algorithms. The minimum-column and row entries for the Traveling Salesman Problem cost matrix provides a powerful heuristic to guide these search techniques. Mission planning subgoals are directed from the planner to the navigator for planning routes in mountainous terrain with threats. Terrain/threat information is abstracted into a graph of possible paths for which graph searches are performed. It is shown that paths can be well represented by a search graph based on the Voronoi diagram of points representing the vertices of mountain boundaries. A comparison of Dijkstra's dynamic programming algorithm and the A* graph search algorithm from artificial intelligence/operations research is performed for several navigation path planning examples. These examples illustrate paths that minimize a combination of distance and exposure to threats. Finally, the pilot system synthesizes the flight trajectory by creating the control commands to fly the aircraft.
Krozel, James A.↗
Expert system validation in prolog
An overview of the Expert System Validation Assistant (EVA) is being implemented in Prolog at the Lockheed AI Center. Prolog was chosen to facilitate rapid prototyping of the structure and logic checkers and since February 1987, we have implemented code to check for irrelevance, subsumption, duplication, deadends, unreachability, and cycles. The architecture chosen is extremely flexible and expansible, yet concise and complementary with the normal interactive style of Prolog. The foundation of the system is in the connection graph representation. Rules and facts are modeled as nodes in the graph and arcs indicate common patterns between rules. The basic activity of the validation system is then a traversal of the connection graph, searching for various patterns the system recognizes as erroneous. To aid in specifying these patterns, a metalanguage is developed, providing the user with the basic facilities required to reason about the expert system. Using the metalanguage, the user can, for example, give the Prolog inference engine the goal of finding inconsistent conclusions among the rules, and Prolog will search the graph intantiations which can match the definition of inconsistency. Examples of code for some of the checkers are provided and the algorithms explained. Technical highlights include automatic construction of a connection graph, demonstration of the use of metalanguage, the A* algorithm modified to detect all unique cycles, general-purpose stacks in Prolog, and a general-purpose database browser with pattern completion.
Stock, Todd↗
Navigation path planning for autonomous aircraft - Voronoi diagram approach
The present technique for generating a search graph depicting topologically unique paths around mountain boundaries at constant altitudes involves a description of mountain boundaries as polygons; the search graph is then generated on the basis of a geometric construct. All nodes and arcs of the search graph are guaranteed to lie in free space, thereby ensuring an autonomous aircraft's avoidance of mountain obstacles. The solution path is generated by searching the graph for the optimal path from a start location to a finish location.
Krozel, Jimmy↗
Decomposition Algorithm for Global Reachability on a Time-Varying Graph
A decomposition algorithm has been developed for global reachability analysis on a space-time grid. By exploiting the upper block-triangular structure, the planning problem is decomposed into smaller subproblems, which is much more scalable than the original approach. Recent studies have proposed the use of a hot-air (Montgolfier) balloon for possible exploration of Titan and Venus because these bodies have thick haze or cloud layers that limit the science return from an orbiter, and the atmospheres would provide enough buoyancy for balloons. One of the important questions that needs to be addressed is what surface locations the balloon can reach from an initial location, and how long it would take. This is referred to as the global reachability problem, where the paths from starting locations to all possible target locations must be computed. The balloon could be driven with its own actuation, but its actuation capability is fairly limited. It would be more efficient to take advantage of the wind field and ride the wind that is much stronger than what the actuator could produce. It is possible to pose the path planning problem as a graph search problem on a directed graph by discretizing the spacetime world and the vehicle actuation. The decomposition algorithm provides reachability analysis of a time-varying graph. Because the balloon only moves in the positive direction in time, the adjacency matrix of the graph can be represented with an upper block-triangular matrix, and this upper block-triangular structure can be exploited to decompose a large graph search problem. The new approach consumes a much smaller amount of memory, which also helps speed up the overall computation when the computing resource has a limited physical memory compared to the problem size.
Kuwata, Yoshiaki↗
Assembly, disassembly and repair of large truss structures in space
This paper addresses the problem of planning assembly, disassembly and repair sequences for large truss structures in space. First, the AND/OR graph representation scheme for mechanical assemblies is reviewed and extended to truss structures. The assembly, disassembly and repair sequence planning problem is then formulated as a graph search problem using assembly's AND/OR graph and appropriate cost functions. The general search problem, which is known to be exponential, is simplified by taking advantage of the symmetries that exist in truss structures. General cost functions for truss assembly are discussed.
Desai, Rajiv S.↗
Global time optimal motions of robotic manipulators in the presence of obstacles
A practical method to obtain the global time optimal motions of robotic manipulators is presented. This method takes into account the nonlinear manipulator dynamics, actuator constraints, joint limits, and obstacles. Previously developed methods of optimizing manipulator motions along given paths and a local path optimization are utilized. A set of best paths is obtained first in a global search over the manipulator workspace, using graph search and hierarchical pruning techniques. These paths are used as initial conditions for a continuous path optimization to yield the global optimal motion. Examples of optimized motions of a six-degree-of-freedom manipulator, operating in a three-dimensional space with obstacles, are presented.
Shiller, Zvi↗
Path planning for assembly of strut-based structures
A path planning method with collision avoidance for a general single chain nonredundant or redundant robot is proposed. Joint range boundary overruns are also avoided. The result is a sequence of joint vectors which are passed to a trajectory planner. A potential field algorithm in joint space computes incremental joint vectors delta-q = delta-q(sub a) + delta-q(sub c) + delta-q(sub r). Adding delta-q to the robot's current joint vector leads to the next step in the path. Delta-q(sub a) is obtained by computing the minimum norm solution of the underdetermined linear system J delta-q(sub a) = x(sub a) where x(sub a) is a translational and rotational force vector that attracts the robot to its goal position and orientation. J is the manipulator Jacobian. Delta-q(sub c) is a collision avoidance term encompassing collisions between the robot (links and payload) and obstacles in the environment as well as collisions among links and payload of the robot themselves. It is obtained in joint space directly. Delta-q(sub r) is a function of the current joint vector and avoids joint range overruns. A higher level discrete search over candidate safe positions is used to provide alternatives in case the potential field algorithm encounters a local minimum and thus fails to reach the goal. The best first search algorithm A* is used for graph search. Symmetry properties of the payload and equivalent rotations are exploited to further enlarge the number of alternatives passed to the potential field algorithm.
Muenger, Rolf↗
Path planning for robotic truss assembly
A new Potential Fields approach to the robotic path planning problem is proposed and implemented. Our approach, which is based on one originally proposed by Munger, computes an incremental joint vector based upon attraction to a goal and repulsion from obstacles. By repetitively adding and computing these 'steps', it is hoped (but not guaranteed) that the robot will reach its goal. An attractive force exerted by the goal is found by solving for the the minimum norm solution to the linear Jacobian equation. A repulsive force between obstacles and the robot's links is used to avoid collisions. Its magnitude is inversely proportional to the distance. Together, these forces make the goal the global minimum potential point, but local minima can stop the robot from ever reaching that point. Our approach improves on a basic, potential field paradigm developed by Munger by using an active, adaptive field - what we will call a 'flexible' potential field. Active fields are stronger when objects move towards one another and weaker when they move apart. An adaptive field's strength is individually tailored to be just strong enough to avoid any collision. In addition to the local planner, a global planning algorithm helps the planner to avoid local field minima by providing subgoals. These subgoals are based on the obstacles which caused the local planner to fail. A best-first search algorithm A* is used for graph search.
Sanderson, Arthur C.↗
HURON (HUman and Robotic Optimization Network) Multi-Agent Temporal Activity Planner/Scheduler
HURON solves the problem of how to optimize a plan and schedule for assigning multiple agents to a temporal sequence of actions (e.g., science tasks). Developed as a generic planning and scheduling tool, HURON has been used to optimize space mission surface operations. The tool has also been used to analyze lunar architectures for a variety of surface operational scenarios in order to maximize return on investment and productivity. These scenarios include numerous science activities performed by a diverse set of agents: humans, teleoperated rovers, and autonomous rovers. Once given a set of agents, activities, resources, resource constraints, temporal constraints, and de pendencies, HURON computes an optimal schedule that meets a specified goal (e.g., maximum productivity or minimum time), subject to the constraints. HURON performs planning and scheduling optimization as a graph search in state-space with forward progression. Each node in the graph contains a state instance. Starting with the initial node, a graph is automatically constructed with new successive nodes of each new state to explore. The optimization uses a set of pre-conditions and post-conditions to create the children states. The Python language was adopted to not only enable more agile development, but to also allow the domain experts to easily define their optimization models. A graphical user interface was also developed to facilitate real-time search information feedback and interaction by the operator in the search optimization process. The HURON package has many potential uses in the fields of Operations Research and Management Science where this technology applies to many commercial domains requiring optimization to reduce costs. For example, optimizing a fleet of transportation truck routes, aircraft flight scheduling, and other route-planning scenarios involving multiple agent task optimization would all benefit by using HURON.
Hua, Hook↗
Decomposition Algorithm for Global Reachability Analysis on a Time-Varying Graph with an Application to Planetary Exploration
Hot air (Montgolfiere) balloons represent a promising vehicle system for possible future exploration of planets and moons with thick atmospheres such as Venus and Titan. To go to a desired location, this vehicle can primarily use the horizontal wind that varies with altitude, with a small help of its own actuation. A main challenge is how to plan such trajectory in a highly nonlinear and time-varying wind field. This paper poses this trajectory planning as a graph search on the space-time grid and addresses its computational aspects. When capturing various time scales involved in the wind field over the duration of long exploration mission, the size of the graph becomes excessively large. We show that the adjacency matrix of the graph is block-triangular, and by exploiting this structure, we decompose the large planning problem into several smaller subproblems, whose memory requirement stays almost constant as the problem size grows. The approach is demonstrated on a global reachability analysis of a possible Titan mission scenario.
Dijkstra's algorithm↗
Sequential Testing Algorithms for Multiple Fault Diagnosis
In this paper, we consider the problem of constructing optimal and near-optimal test sequencing algorithms for multiple fault diagnosis. The computational complexity of solving the optimal multiple-fault isolation problem is super-exponential, that is, it is much more difficult than the single-fault isolation problem, which, by itself, is NP-hard. By employing concepts from information theory and AND/OR graph search, we present several test sequencing algorithms for the multiple fault isolation problem. These algorithms provide a trade-off between the degree of suboptimality and computational complexity. Furthermore, we present novel diagnostic strategies that generate a diagnostic directed graph (digraph), instead of a diagnostic tree, for multiple fault diagnosis. Using this approach, the storage complexity of the overall diagnostic strategy reduces substantially. The algorithms developed herein have been successfully applied to several real-world systems. Computational results indicate that the size of a multiple fault strategy is strictly related to the structure of the system.
Shakeri, Mojdeh↗
Experiments with a decision-theoretic scheduler
This paper describes DTS, a decision-theoretic scheduler designed to employ state-of-the-art probabilistic inference technology to speed the search for efficient solutions to constraint-satisfaction problems. Our approach involves assessing the performance of heuristic control strategies that are normally hard-coded into scheduling systems, and using probabilistic inference to aggregate this information in light of features of a given problem. BPS, the Bayesian Problem-Solver, introduced a similar approach to solving single-agent and adversarial graph search problems, yielding orders-of-magnitude improvement over traditional techniques. Initial efforts suggest that similar improvements will be realizable when applied to typical constraint-satisfaction scheduling problems.
Hansson, Othar↗
Decision-theoretic control of EUVE telescope scheduling
This paper describes a decision theoretic scheduler (DTS) designed to employ state-of-the-art probabilistic inference technology to speed the search for efficient solutions to constraint-satisfaction problems. Our approach involves assessing the performance of heuristic control strategies that are normally hard-coded into scheduling systems and using probabilistic inference to aggregate this information in light of the features of a given problem. The Bayesian Problem-Solver (BPS) introduced a similar approach to solving single agent and adversarial graph search patterns yielding orders-of-magnitude improvement over traditional techniques. Initial efforts suggest that similar improvements will be realizable when applied to typical constraint-satisfaction scheduling problems.
Hansson, Othar↗
Path Planning with obstacle avoidance
The research report here summarizes a solution for two dimensional Path Planning with obstacle avoidance in a workspace with stationary obstacles. The solution finds the shortest path for the end effector of a manipulator arm. The program uses an overhead image of the robot work space and the starting and ending positions of the manipulator arm end effector to generate a search graph which is used to find the shortest path through the work area. The solution was originally implemented in VAX Pascal, but was later converted to VAX C.
Krause, Donald M.↗
Learning dominance relations in combinatorial search problems
Dominance relations commonly are used to prune unnecessary nodes in search graphs, but they are problem-dependent and cannot be derived by a general procedure. The authors identify machine learning of dominance relations and the applicable learning mechanisms. A study of learning dominance relations using learning by experimentation is described. This system has been able to learn dominance relations for the 0/1-knapsack problem, an inventory problem, the reliability-by-replication problem, the two-machine flow shop problem, a number of single-machine scheduling problems, and a two-machine scheduling problem. It is considered that the same methodology can be extended to learn dominance relations in general.
Yu, Chee-Fen↗
Autonomous star identification for spacecraft attitude control
Research is being conducted to enhance the Advanced Star and Target Reference Optical Scanner (ASTROS I) so that it will be able to automatically track a star and recognize the star's pointing position. Previously developed field identification algorithms, coded on a flight-scale computer, are linked to a breadboard ASTROS star tracker to calculate pointing vectors in real time. A simple graph-searching algorithm was used in an initial study to find stellar positions based on pattern recognition. Results from this study and plans for further development are presented.
Rappaport, Barry↗
Assembly planning for large truss structures in space
The approach is based on a graph search algorithm. A relational data structure is used to represent a truss structure. There are four types of entities: units, faces, edges, and vertices. There are contain/contained relationships for every pair of entity types, as well as in-contact relationships between faces. A best-first algorithm constitutes the core of the planner. The cost function in the current implementation corresponds to a combination of the rigidity of the intermediate structures and the total distance to be traversed by the agent executing the assembly tasks.
Homem De Mello, L. S.↗