Artificial Intelligence: Methods and applications Lecture 6: Path planning Ola Ringdahl Umeå University November 21, 2014
Navigation Four questions: • Where am I going? – Mission planning (human or planner) • What is the best way to get there? – Path planning (Topological or Metric) • Where have I been? – Map making • Where am I now? – Localization (relative or absolute) Artificial Intelligence: Methods and applications 2 Ola Ringdahl, Umeå University
Spatial Memory • The answer to “What’s the Best Way There?” depends on the representation of the world • A robot’s world representation is its spatial memory. It support the following functions: – Attention: What features to look for next? – Reasoning: Can this surface support my weight? – Path planning: What’s the best way ? – Information collection: What has changed since last time I was here? Artificial Intelligence: Methods and applications 3 Ola Ringdahl, Umeå University
Two forms of Spatial Memory Based on landmarks (qualitative/ Topological ) Based on regular maps ( quantitative/ Metric ) Artificial Intelligence: Methods and applications 4 Ola Ringdahl, Umeå University
Topological Spatial Memory • Express space in terms of connections between landmarks • From the robot’s perspective – Identification of landmarks – Orientation clues, e.g. “to the left” • Usually cannot be used to generate metric representations Artificial Intelligence: Methods and applications 5 Ola Ringdahl, Umeå University
Metric Spatial Memory • Express space in terms of physical distances of travel: A metric map • Bird’s eye view of the world • Not dependent upon the perspective of the robot – Independent of orientation and position of robot • Can also be used to generate topological representations Artificial Intelligence: Methods and applications 6 Ola Ringdahl, Umeå University
9. TOPOLOGICAL PATH PLANNING USE A TOPOLOGICAL SPATIAL MEMORY 7
Landmarks One or more perceptually distinctive features of interest on an object or area of interest • Natural landmark : wasn’t put in the environment to aid with the robot’s navigation (e.g. tower, corner, tree, doorway) • Artificial landmark : added to the environment to support navigation (e.g. highway sign, RFID tags) Try to avoid artificial landmarks! Artificial Intelligence: Methods and applications 8 Ola Ringdahl, Umeå University
Desirable Characteristics of Landmarks • Recognizable - From sufficiently long range - From different viewpoints • Supply necessary information - Identity (unique globally or at least locally) - Relative orientation and distance to the landmark - … Artificial Intelligence: Methods and applications 9 Ola Ringdahl, Umeå University
Two types of Topological navigation methods • Relational - spatial memory (known as a topological map or relational graph) is based on landmarks - use graph theory to plan paths • Associative - spatial memory is a series of remembered viewpoints, where each viewpoint is labeled with a location - good for retracing steps Artificial Intelligence: Methods and applications 10 Ola Ringdahl, Umeå University
Constructing a Topological map • Draw edges and nodes to cover the area • Nodes: – possible goals or gateways (where the direction may change) • Edges: – Navigable paths between nodes Room 1 Room 2 Room 3 Room 4 Artificial Intelligence: Methods and applications 11 Ola Ringdahl, Umeå University
Problems with relational graphs • The graph is not coupled with information on how to get from one node to another • Dead reckoning accumulates uncertainty – Possible solution: add localization to landmarks • Hard to find good distinctive places (features/landmarks) Artificial Intelligence: Methods and applications 13 Ola Ringdahl, Umeå University
Topological Path Planning Algorithms • Answers “What’s the best way there?” • Find a sequence of nodes that leads you to the goal! • Relational graph, so any shortest path algorithm will work, e.g. Dijkstra’s algorithm Artificial Intelligence: Methods and applications 14 Ola Ringdahl, Umeå University
Two types of Topological navigation methods • Relational - spatial memory is based on landmarks (also known as a topological map or relational graph) - use graph theory to plan paths • Associative - spatial memory is a series of remembered viewpoints, where each viewpoint is labeled with a location - good for retracing steps (Path Tracking) - converts sensor observations to direction Artificial Intelligence: Methods and applications 15 Ola Ringdahl, Umeå University
Associative Method example 1 • Visual Homing - bees navigate to their hive by a series of image signatures which are locally distinctive (within a neighborhood) Artificial Intelligence: Methods and applications 16 Ola Ringdahl, Umeå University
Image Signatures for Visual Homing The world Tessellated (like faceted-eyes) Resulting signature for home Artificial Intelligence: Methods and applications 17 Ola Ringdahl, Umeå University
Image Signatures for Visual Homing Move to match the template Artificial Intelligence: Methods and applications 18 Ola Ringdahl, Umeå University
Associative Method example 2 • QualNav • Developed as a military project - The UGV had to check an area and return home without being seen: i.e: had to move far away from potential landmarks Artificial Intelligence: Methods and applications 19 Ola Ringdahl, Umeå University
QualNav OR2 OR1 mountain building radio tree tower • Works out-doors with landmarks far away • Landmark pair boundary: Imaginary line drawn between 2 landmarks. Partitions the world into Orientation regions (OR). Artificial Intelligence: Methods and applications 20 Ola Ringdahl, Umeå University
QualNav OR2 OR1 Topological map mountain Metric building Map radio tree tower • Within an OR: to localize the robot, use recorded angles to the landmarks (viewframe) • When the robot moves from one OR to another, the border Landmark pair boundaries will move in front /on the side/behind. No distances needed. Artificial Intelligence: Methods and applications 21 Ola Ringdahl, Umeå University
Summary Topological Path Planning • Navigating by detecting and responding to landmarks. • Landmarks may be natural or artificial • Two types of topological path planning – Relational – Associative Artificial Intelligence: Methods and applications 22 Ola Ringdahl, Umeå University
Summary Topological Path Planning • Relational methods – spatial memory is based on landmarks – use graph theory to plan paths in the topological map • Associative methods – remember places as image signatures or as extracted viewframes – direct stimulus-response coupling by matching perception to signature to response – Assume perceptual stability and perceptual distinguishability – Sensitive to changes in the world Artificial Intelligence: Methods and applications 23 Ola Ringdahl, Umeå University
10 METRIC PATH PLANNING USE A METRIC SPATIAL MEMORY 24
Metric Path Planning • Determine a path from one point to goal – Generally interested in “ best ” or “ optimal ” – What are measures of best/optimal? • Path planning assumes an a priori map of relevant aspects – Relevant: occupied or empty – Looks like a “ bird ’ s eye ” view, position & viewpoint independent • We will look at Representations and Algorithms Artificial Intelligence: Methods and applications 25 Ola Ringdahl, Umeå University
REPRESENTATIONS FOR METRIC PATH PLANNING Artificial Intelligence: Methods and applications 26 Ola Ringdahl, Umeå University
World Space & Cspace • World Space: physical space robots and obstacles exist in – (x,y,z) plus three angles: 6DOF. • Configuration Space (Cspace) – A transformation into a representation suitable for planning, simplifying assumptions, e.g. fewer DOFs: 6DOF 2 or 3 DOF – Or considering only a limited number of poses (grids and graphs) Artificial Intelligence: Methods and applications 27 Ola Ringdahl, Umeå University
Cspace Representations • Idea: reduce world space to a Cspace representation which is more suitable for storage in computers and for rapid execution of path planning algorithms • Major types – Meadow Maps – Generalized Voronoi Graphs (GVG) – Regular grids, quadtrees Artificial Intelligence: Methods and applications 28 Ola Ringdahl, Umeå University
Meadow Maps • Example of the basic procedure of transforming world space to cspace • Step 1 (optional): grow obstacles as big as robot Artificial Intelligence: Methods and applications 29 Ola Ringdahl, Umeå University
Meadow Maps cont. • Step 2: Construct convex polygons as line segments between pairs of corners, edges – Why convex polygons? Interior has no obstacles so can safely transit (“freeway”, “free space”) Artificial Intelligence: Methods and applications 30 Ola Ringdahl, Umeå University
Meadow Maps cont. • Step 3: Convert to a relational graph by connecting midpoints of lines of the polygons • A search algorithm can now find the ”optimal” path Artificial Intelligence: Methods and applications 31 Ola Ringdahl, Umeå University
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