1. Robotics Reprise: piano movers’ problem. Locomotion Lab session Homework: postings. Work on projects.

2. Complexity Study of how long problem can take Example: certain sorts may take up to square of N steps, for input size N; others take less: N*log 2 (N). Binary search (dividing the search space) means that any search limited by log 2 (N) steps.

3. NP complete problems There is a set of problems for which there hasn’t been found a good solution. –Where good means doing in polynomial time. Solutions for these problems can be checked in polynomial time. Examples: graph coloring, traveling salesman, logical satisfiability If one of these problems can be done, they all can be done.

4. The piano movers’ problem Moving something, such as a robot with payload (what it needs to carry) through a space with obstacles. Aka Motion planning General problem is at least as hard as NP complete problems and may be harder! One approach is to grow the obstacles while shrinking the robot and then go from corner to corner

5. Locomotion What is the problem What is requirement for stability –Static stability: capacity to return to standing if moved slightly –Dynamic stability: capacity while moving to return to (steady, desired) movement when pushed What (where) is the control –What are the levels of control May have high-level goal supplied and then device achieves that goal through local action

6. Distinct problems/challenges: Navigate over a particular terrain Level, smooth floors inside building –robot competitions –Manufacturing –Homes, hospitals, nursing homes, etc. Streets –light payloads –Heavy/heavier payload: autonomous cars In and out of streets & buildings –Rescue, detecting and disarming bombs, … Ground (including moon, Mars, etc.)

7. More challenges Combine travel over floor with climbing stairs in buildings (and other tasks such as climbing walls?) Imitate human locomotion –to replace [human] stuntman in movies –for testing of shoes and other gear More ???

8. Different problem: Prosthetic limbs Varying need to resemble somewhat what is being replaced vs Specialization for task –Sports limbs: Already controversy: double leg replacement allowed for longer legs http://www.spectrum.ieee.org/jun05/1217 Oscar Pistorius

9. Skiing Trak III: –Remove leg and use outriggers –Critical issue is how to remove, protect stump and then re-attach limb

10. Skiing Sit ski

11. Artificial limbs issues Physical connection to body –Permanent? –Temporary but want long duration Control connection to nervous system for control –Same –Other Sensory input for performance of task

12. Hand Goal is for hand to be able to grasp without crushing object or letting it slip http://www.newscientisttech.com/article/dn1 0785-robotic-hand-has-a-builtin-slip- sense.html

13. Serpentine Problems –Surgery –Disarm bombs, mines Land or water –Rough terrain http://www.primidi.com/2005/03/23.html

14. Note Many of the experimental robots still are controlled teleoperator fashion Though…some have complex distributed control systems

15. Mobile robot (Ralph Hollis) http://www.msl.ri.cmu.edu/projects/ General goal: mobile, dynamically stabile agile to be personal assistant

16. Robots in Scansorial Environment (also Hollis lab) 6 legged climbing machine

17. Haptic devices Touch contact force Note: may always be contact, for example, air, breeze. May need to quantify to distinguish.

18. Lab & Homework Continue to work on building project Postings