Algorithmic Robotics and Motion Planning Dan Halperin Tel Aviv University Fall 2006/7 Introduction abridged version

Robots, take I

An extremely brief history of robotics The RUR robot which appeared in an adaption of Czech author Karel Capek's Rossum's Universal Robots. Circa 1930's. For more, see, e.g., pages.cpsc.ucalgary.ca/~jaeger/visual Media/robotHistory.html UNIMATE becomes the first industrial robot in use. It was used at the General Motors factory in New Jersey. NASA's PathFinder lands on Mars,1997 Honda ’ s ASIMO 2002

Motion planning: the basic problem Let B be a system (the robot) with k degrees of freedom moving in a known environment cluttered with obstacles. Given free start and goal placements for B decide whether there is a collision free motion for B from start to goal and if so plan such a motion.

A disc moving among discs ?

Terminology  Workspace  Configuration  Degree of freedom (dof)

Configuration space of a robot system with k degrees of freedom  the space of parametric representation of all possible robot configurations  C-obstacles: the expanded obstacles  the robot -> a point  k dimensional space  point in configuration space: free, forbidden, semi-free  path -> curve

C-obstacles Q - a polygonal object that moves by translation P - a set of polygonal obstacles reference point

Minkow s ki sums and translational C-obstacles  A  B= {a+b | a  A, b  B}  Let -A denote A with the ref point at the origin and rotated by 180 deg around the origin  The robot A(q) intersects the obstacle B iff q  B  -A  Minkowski sums of convex polygons: complexity and construction

More complex systems  Already in the plane, if we allow rotation as well, the problem has 3 dofs  Bodies translating and rotating in 3-space  Industrial manipulators (typically have 4,5, or 6 dofs)  New designs, multi-robot systems, and other moving artifacts have many more dofs

Types of solutions  Exact  Heuristic  Hybrid  A major component in practical solutions: collision detection

Cluterred environments

Oskar

Algorithmic robotics, automation assembly planning  Movable separability  Assembly planning with two hands  Motion space [Snoeyink-Stolfi 93]

Robots, take II

Beyond the basic mop problem  Moving obstacles  Multiple robots  Movable objects  Uncertainty  Nonholonomic constraints  Dynamic constraints  …

Optimality, path quality  Length  Clearance  Group motion: tradeoff Kamphuis-Overmas,

Kinematics  Link  Joint  Base  Tcp  Kinematic chain  Direct kinematics  Inverse kinematics

Robots with many dofs

Sensorless manipulaion Example: the parallel jaw gripper [Goldberg]

Course outline see

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