1. Hybrid Architectures Today: More Planning Tuesday: Examples of Hierarchical Systems Hand-out Midterm How can "natural" interaction with a robot be designed?

2. Pathing: Deliberative Navigation How do you get from point A to point B? –Consider possible paths before moving –Representation of the world –Search through a state space

3. Search: A* f(n) = g(n) + h(n) –g(n) Cost of going from the starting state to state n –h(n) heuristic estimate of the cost of going from state n to the goal state Guaranteed to find a solution if one exists Will find optimal solution –Heuristic must be admissible Variations –IDA* (Iterative Deepening) –Bi-directional –D* (Dynamic Planning) –Hierarchical A*

4. Admissible Heuristics for Pathing Straight Line Distance h(A) = sqrt((A.x-goal.x)^2 + (A.y-goal.y)^2) Manhattan Distance h(A) = (abs(A.x-goal.x) + abs(A.y-goal.y)) Diagonal Distance h(A) = max(abs(A.x-goal.x), abs(A.y-goal.y)) Adjust the magnitude by a heuristic weighting factor to estimate the cost of traversing the terrain.

5. A* Primer Create a node containing the goal state node_goal Create a node containing the start state node_start Put node_start on the open list While the OPEN list is not empty { Get the node off the open list with the lowest f-value and call it node_current Of node_current is the same state as node_goal we have found the solution; return solution Generate each state node_successor that can come after node_current For each node_successor of node_current { Set the cost of this node to be the cost of node_current plus the cost to get to node_successor If this node is on the OPEN list but the existing one is better then discard this successor; break If this node is on the CLOSED list but the existing one is better then discard this successor; break Remove occurrences of this state from OPEN and CLOSED Set the parent of node_successor to node_current Set h-value to be the estimated distance to node_goal Add this node to the OPEN list by f-value } Return failure Do you have to have an OPEN and CLOSED list?

6. A* Example: European Vacation

7. On the Road to Bucharest A* Pathing: Arad to Bucharest

8. Overestimating the Heuristic A* chooses which location to expand based on the value f(n) = g(n) + h(n) If h(n) is admissible, A* will generate all paths that underestimate the actual path cost, thereby guaranteeing that the solution path found is the optimal one.

9. Additional Points Cost of Travel –Additional costs associated with path or region. –Terrain –Uphill & down hill costs A good heuristic estimate will expand fewer nodes –If h 2 (n) >= h 1 (n) for all n then h 2 dominates h 1 –If both are admissible h 1 will expand as many or more nodes than h 2 An efficient data structure is important for storing the Open and Close lists. A* Demo

10. World Representations

11. Obstacles What should the robot do if it cannot complete the plan? Algorithm Complexity –Time ? –Space? –Ways to reduce?

12. Knowledge Representation for Task Plans Knowledge Representation Language KRL = Representation + Inference Method Representation: Language for representing facts about the domain Inference: method(s) for establishing new facts from known facts The store of agent’s knowledge is termed its “knowledge base” –Derived from the idea of a data base –“Knowledge-Based Agents”

13. KRL: Syntax & Semantics Syntax Rule for constructing valid sentences. Valid configuration of symbols that constitute a sentence. Example: X >= YValid Math Sentence =XY>Invalid Math Sentence

14. Example Syntax

16. KRL: Syntax & Semantics Semantics “Meaning” of a sentence. Determines the facts in the agent’s world to which the sentence refers. What an agent “believes”. Example: X >= YFalse if Y is bigger than X True if otherwise

17. KRL Limitations to Meaning

18. Where does meaning come from? What the agent understands: For defeating the blob Gandolf gets: 2 gold * 45 gold Gandolf’s gold = 90 gold What we understand: If nothing is on top of BLOCK_A then BLOCK_A can be picked up If the DOOR between CURRENT_ROOM and NEXT_ROOM is open then NEXT_ROOM can be entered Symbol Grounding Problem –A symbol system is a set of symbols that can be operated on by a set of rules (KRL). There is no need to make use of the meaning, only the syntax. So where does the meaning come from?

19. Planning A plan is a sequence of actions that achieves a goal

20. Approaches to Planning State-space search –Search through the possible future states that can be reached by applying different sequences of actions Plan-space Search –Search through possible plans by applying operators that modify plans

21. STRIPS Planner STRIPS operators –Pre-conditions: what must be true so I can take this action –Deletions: what must be deleted if action is taken –Additions: what must be added if action is taken

23. Means-Ends Analysis