Cluster Subgraphs Example, With Tile Graphs. Alternatives. Cluster Subgraphs. Cluster Subgraphs Example, With Tile Graphs

Transcription

1 Alternatives Cluster Subgraphs Example, With Tile Graphs Replace a cluster with a small subgraph instead of a single node. e.g. represent entry/exit points run path-finding on the abstract graph to find high-level route run path-finding within each cluster to find low-level details of route CPSC 444: Artificial Intelligence Spring CPSC 444: Artificial Intelligence Spring Cluster Subgraphs Example, With Tile Graphs Cluster Subgraphs Advantages: more accurate edge costs can capture actual distance between entry/exit points within a cluster may still need a heuristic if multiple entry/exit points are combined into one node clusters are defined by a larger-scale grid identify connections between clusters small entrances single connection edge large entrances two connection edges, one at each end edge costs = shortest path between nodes use pathfinding to compute Disadvantages: multiple nodes per cluster larger graph CPSC 444: Artificial Intelligence Spring CPSC 444: Artificial Intelligence Spring

2 Variations on Pathfinding Dynamic Pathfinding open goal planning find a goal rather than the goal dynamic pathfinding pathfinding in a changing world continuous time pathfinding pathfinding with fine-grained control over when decisions are made movement planning find a legal sequence of movements in domains where agents can't steer along arbitrary paths Pathfinding may take place in a world where the environment is changing and/or not everything is known about the state of the world. Simple solution. plan based on current state/knowledge, then re-plan when it is detected that things have changed CPSC 444: Artificial Intelligence Spring CPSC 444: Artificial Intelligence Spring Open Goal Planning Dynamic Pathfinding looking for a goal rather than the goal This requires the heuristic to report distance to nearest goal. increases the work to evaluate the heuristic e.g. compute for each goal, then take minimum inaccuracies in h(n) can lead to wasted time searching near goal thought to be closer Typically addressed by having decision-maker decide on the goal. pathfinder simply finds route to specified goal can be too expensive to replan if change is frequent Alternatives. use other algorithms e.g. D*, a dynamic version of A* can accommodate changing edge weights tradeoff is increased storage space to keep track of information that might be required later CPSC 444: Artificial Intelligence Spring CPSC 444: Artificial Intelligence Spring

3 Continuous Time Pathfinding So far we've assumed that the choices being made occur at specific times and locations. e.g. move from one tile / waypoint / polygon to another More flexibility is needed when the task changes frequently. e.g. a car driving in traffic on a multi-lane highway pathfinding task is to determine when/where to change lanes Solution attempt. shrink the spacing of the nodes results in a larger graph, which impacts efficiency ultimately there are an infinite number of states Millington and Funge, Artificial Intelligence for Games CPSC 444: Artificial Intelligence Spring CPSC 444: Artificial Intelligence Spring Solution attempt. build a graph by placing nodes at intervals in each lane connect consecutive nodes within a lane connect nodes in adjacent lanes gaps for lane-changing may be narrow may be missed if nodes are not placed just right or not placed frequently enough may get abrupt swerves when nodes line up, but aren't well-spaced in the interval Another wrinkle. A* relies on the cost of edge (u,v) being the same regardless of the path taken to get to u in traffic, timing is everything a gap may only exist if you arrive at the point at the right time CPSC 444: Artificial Intelligence Spring CPSC 444: Artificial Intelligence Spring

4 Graph Graph Generation To address variable weights: nodes in the navigation graph will represent particular positions at particular times multiple nodes to represent the same position at different times include edge (u,v) only if v can be reached from u and the time is correct A* can be used Millington and Funge, Artificial Intelligence for Games infinite states and multiple copies of each: dynamically generate only the subsection of the pathfinding graph that is needed seek to reduce the branching factor CPSC 444: Artificial Intelligence Spring Dynamically generate the graph. start with a single node: (current location, current time) generate additional nodes and connections on demand boundary node immediately behind the next car in the current lane assume car travels as fast as possible, then slows at the last minute to match speed of next car omit if there's no way to avoid collision e.g. already too close to slow enough lane change nodes one for each vacant adjacent lane opportunity nodes in the current lane, immediately after passing each car in each adjacent lane, until reaching the next car in the current lane safe opportunity nodes assume car travels as fast as possible, then slows at the last minute to match speed of next car ahead unsafe opportunity nodes assume car travels as fast as possible in all cases, consider the position of the other car when it would be reached rather than its current position CPSC 444: Artificial Intelligence Spring Graph Graph Generation Seek to reduce the branching factor by constraining the possible nodes and connections. assume lane changes happen as soon as possible no disadvantage; delaying may miss opportunities assume car travels as quickly as possible in its lane may be realistic, but not always the best strategy Millington and Funge, Artificial Intelligence for Games moving ahead to the first gap in lane 2 means missing the gap in lane 3 waiting for the second gap to catch up means that it will be possible to make the gap in lane 3 Rationale. boundary node immediately behind the next car in the current lane allows for not changing lanes lane change nodes one for each vacant adjacent lane allows for immediate lane change opportunity nodes in the current lane, immediately after passing each car in each adjacent lane, until reaching the next car in the current lane safe opportunity nodes allow for future lane changes unsafe opportunity nodes allow for last-minute swerves CPSC 444: Artificial Intelligence Spring CPSC 444: Artificial Intelligence Spring

5 Edge Cost Edge cost. typically just time goal is to travel as quickly as possible can include other factors e.g. risk of collision, to allow dangerous maneuvers only if there's a great advantage or no other alternative CPSC 444: Artificial Intelligence Spring