Manipulation By PushingIntroductionSlide 3Configuration Space vs. Work SpaceConstraintsConstraints Are Your FriendSlide 7Slide 8Slide 9Constraint TaxonomyHolonomic vs. Non-HolonomicGraspingSlide 13Slide 14Slide 15Taxonomy of ContactsGrasp Analysis: Reuleaux’s MethodSlide 18Slide 19Slide 20Slide 21Slide 22Slide 23Motion Path PlanningSlide 25Slide 26Slide 27Motion Path Planning: Visibility GraphMotion Path Planning: Best First Search (& Friends)Slide 30Rapidly-exploring Random TreesRRT Search AlgorithmRapidly Exploring Random TreesRRT-ConnectPath SmoothingPathsMotion Path Planning: Potential FieldsSlide 38Slide 39Motion Path Planning: SummaryNext Time:115-494 Cognitive Robotics03/30/09Manipulation By Pushing15-494 Cognitive Robotics David S. Touretzky & Ethan Tira-Thompson Carnegie Mellon Spring 2009215-494 Cognitive Robotics03/30/09Introduction•Affordances are where we want to be•Kinematics are where we are•How do we get from basic kinematics to actually doing something?315-494 Cognitive Robotics03/30/09Introduction•How do we get from basic kinematics to actually doing something?•Configuration Space vs. Work Space•Constraints•Form Closure vs. Force Closure•Grasp Analysis (Reuleaux’s Method)•Path Planning•Cspace, visibility graph, best first, RRT415-494 Cognitive Robotics03/30/09Configuration Spacevs. Work Space•Consider a 2-link arm, with joint constraints:0° <0 < 90° , -90° < 1 < 90°Configuration Space: robot’s internal state space (e.g. joint angles)Work Space: set of all possible end-effector positions515-494 Cognitive Robotics03/30/09Constraints•Constraints can be your friend!•Upside: Use the environment and the object itself to your advantage.•Downside: Requires planning and accurate modeling•Example: Part Orientation•Can position/orient an ‘L’ shaped part with unknown initial configuration using nothing more than an actuated tray — no sensors!615-494 Cognitive Robotics03/30/09QuickTime™ and aVideo decompressorare needed to see this picture.•Example: Part OrientationConstraints Are Your FriendFujimori, T., Development of Flexible Assembly System “SMART”Video of Sony SMART Cell demo system by Wes HuangCMU Manipulation LabFujimori, T., Development of Flexible Assembly System “SMART”Video of Sony SMART Cell demo system by Wes HuangCMU Manipulation Lab715-494 Cognitive Robotics03/30/09Constraints Are Your Friend•Example: Throwing (Kevin Lynch)815-494 Cognitive Robotics03/30/09QuickTime™ and aCinepak decompressorare needed to see this picture.A Turn and Two TopplesTom A. ScharfeldKevin M. LynchDecember 2, 1998A Turn and Two TopplesTom A. ScharfeldKevin M. LynchDecember 2, 1998Constraints Are Your Friend•2 DOF Arm over a conveyor belt (2JOC)915-494 Cognitive Robotics03/30/09QuickTime™ and aH.263 decompressorare needed to see this picture.Constraints Are Your Friend•Example: Hinge AssemblyPingle, K., Paul, R., Bolles, R., "Programmable Assembly, Three Short Examples," Film,Stanford Artificial Intelligence Laboratory, October 1974.Pingle, K., Paul, R., Bolles, R., "Programmable Assembly, Three Short Examples," Film,Stanford Artificial Intelligence Laboratory, October 1974.1015-494 Cognitive Robotics03/30/09Constraint Taxonomy•Bilateral - expressed by equality (e.g. y = 0)•Unilateral - expressed by inequality (e.g. y > 0)•Scleronomic - independent of time (static)•Rheonomic - changes over time (e.g. θ=2πt)•Holonomic - all constraints are independent of rate of change and bilateral (direct mapping between configuration space and work space)1115-494 Cognitive Robotics03/30/09Holonomic vs. Non-Holonomic•Holonomic: robotic arms, unsteered mobile robots, omni-directional mobile robots•can define configuration space such that returning to a configuration point implies returning to consistent point in work space•Non-Holonomic: commonly, mobile robots with constraints on their instantaneous motion, e.g. unicycles, steered carts (Ackerman steering) can’t go sideways1215-494 Cognitive Robotics03/30/09Grasping•What does it mean to “hold” something?•Form closure: object is “secure” — can’t move without moving a contact point•Force closure: can apply any desired force•Not necessarily the same thing — depends on your friction model (next lecture)No friction:Form closure, but no force closureWith friction:Force closure, but no form closure1315-494 Cognitive Robotics03/30/09•Form closure is defined in increasing orders: position, velocity, acceleration, etc.•Force closure does not have orders (you have it or you don’t)•Frictionless force closure equates tofirst-order (positional) form closureGraspingExample grasp with both force closure and first-order form closure, regardless of frictional model1415-494 Cognitive Robotics03/30/09•Original examples do not have force closure•Left figure can be moved infinitesimally up or down, although cannot be in motion vertically (so it has second-order form closure)GraspingWith no friction,neither example has force closure norfirst-order form closure1515-494 Cognitive Robotics03/30/09Grasping•What does it mean to “hold” something?•Form closure: object is “secure” — can’t move without moving a contact point•Force closure: can apply any desired force•Equilibrium: can resist environmental forces (gravity)•Stability: how much variance from the environment can be tolerated and still maintain equilibrium15-494 Cognitive Robotics03/30/0916Taxonomy of ContactsFigure 4.8 - Mason, Mechanics Of Robotic Manipulation1715-494 Cognitive Robotics03/30/09•For each constraint, divide the plane into areas which can hold positive or negative centers of rotation (IC’s - instantaneous centers)Grasp Analysis:Reuleaux’s Method+–±1815-494 Cognitive Robotics03/30/09•Intersect common regionsGrasp Analysis:Reuleaux’s Method+–1915-494 Cognitive Robotics03/30/09•Intersect common regionsGrasp Analysis:Reuleaux’s Method++––2015-494 Cognitive Robotics03/30/09•Another example:•Is this completely constrained?Grasp Analysis:Reuleaux’s Method2115-494 Cognitive Robotics03/30/09•Another example:•Can spin counter-clockwise around area in the middle — but not clockwise!Grasp Analysis:Reuleaux’s Method++2215-494 Cognitive Robotics03/30/09•How about now?•Common intersections may indicate, butdo not guarantee, that rotation is possibleGrasp Analysis:Reuleaux’s Method2315-494 Cognitive Robotics03/30/09Grasp