HIGH-LEVEL ROBOT ARM MANIPULATION PRIMITIVESOutlineIntroductionSlide 4Slide 5Slide 6Problem StatementBackgroundThree-Link Planar ArmManipulation SurfacesWhy not two links?Why not four or more links?KinematicsForward KinematicsInverse KinematicsSlide 16IK Calculations ProcessMultiple SolutionsIK ModificationsSlide 20Slide 21Slide 22Slide 23Path PlannerPath PlanningRapidly-exploring Random TreesRRT-ConnectPath SmoothingPathsMethodologyManipulation primitivesHigh-Level PrimitivesSlide 33Slide 34Slide 35Slide 36Manipulation PlannerPlanning Process ComplicationsSlide 39Slide 40Slide 41Executing the PlanManipulation EngineValidation: A tic-tac-toe playerPlaying tic-tac-toeContributions/Expected OutcomeTimeline/MilestonesReferencesQuestionsHIGH-LEVEL ROBOT ARM MANIPULATION PRIMITIVES Thesis Proposal for the Master of Science Degree in Computer Science Presented by Glenn NickensAdvised by Dr. David TouretzkyThursday, January 29, 20091Outline•Introduction to the research topic•Problem statement•Accomplished background work•Proposed method of completion and testing•Expected outcome and contributions•Timeline2Introduction•Access to the field of robotics has been limited in computer science undergraduate programs due to :–The complexity of the underlying mathematics and theory that is needed to implement kinematics, path planning and manipulation –The size, cost and/or limited capabilities of available robots•To help solve this problem, researchers at Carnegie Mellon University have developed:–Tekkotsu–A hand-eye robot3Introduction•Tekkotsu–Is an open source robot programming framework based on C++.–Is an object-oriented and event passing architecture that makes full use of the template and inheritance features of C++ (Tekkotsu).–Programmers use high-level primitives, such as “nod your head” and “walk to that location”, to control robots.4Introduction•The hand-eye robot:–Has a three-link planar arm, with a webcam attached to a pan-tilt above it for vision–Is a small, affordable robot that fits on a classroom table–Can be programmed to manipulate objects identified by the camera•However, Tekkotsu does not have high-level manipulation primitives for an arm.5Introduction•Developing the high-level primitives necessary to perform manipulation with the arm is the subject of this research proposal.•Once the primitives are developed, I will test them by writing a tic-tac-toe player.•The player will use only the primitives developed in this research to manipulate the game pieces. 6Problem StatementTekkotsu does not have the high-level manipulation primitives for a hand-eye robot to perform complex tasks such as moving an object to a target position. In this research I will specify the primitives required to perform complex tasks. I will implement them, then demonstrate that the primitives are suitable for performing the tasks.7Background•To develop the manipulation primitives the following are necessary:–A robot arm–Kinematics–Collision detection–Path planning–Path smoothing8Three-Link Planar Arm•Three Dynamixel AX-12 servos•Upper arm and forearm are constructed of aluminum tubes and elongated c-brackets•End-effector is a c-bracket9Manipulation Surfaces•No closeable fingers•Must move objects by pushing them•Three manipulation surfaces:–Interior of the c-bracket–Wrist–Forearm & Upper arm10Why not two links?•Manipulation in the plane requires at least 3DOF (x, y, and ).•A two-link arm only has 2DOF.•A a three-link arm can reach a target from many angles; a two-link arm can reach it from only two angles.11Why not four or more links?•Given a target and angle of manipulation, a three-link arm will have at most two solutions, a four-link arm may have infinitely many solutions.•Solving kinematics for a four-link arm is more complex than for a three-link arm.•Links are expensive (power, weight, wiring).12Kinematics•Kinematics describes the relationship between the position and orientation of the end-effector and the joint angles of the arm.13Forward Kinematics•Forward/direct kinematics calculations determine the end effector configuration given the joint angles.•Forward kinematics calculations are easily solved with a series of matrix multiplications, and will always produce a unique solution.140)()()()(0)()()()(033213213213212212121211111LcsscLcsscLcsscInverse Kinematics•Inverse kinematics calculations search for a set of joint angles that produce a specified end effector configuration.•Inverse kinematics calculations are harder; there may be many solutions, or there may be none.15Inverse Kinematics•In this research, inverse kinematics is used to determine the shoulder, elbow, and wrist angles given a target position and the manipulation surface orientation.•The inverse kinematics calculations for the arm use a four step process based on a common analytical approach documented in the book ‘Robot Modeling and Control’.16IK Calculations Process1. Determine the wrist position [xw, yw] from the target point [xt, yt] and desired orientation, ϕt.2. Determine the elbow angle, θ2, from the wrist position [xw, yw] and arm dimensions, L1 and L2.3. Determine the shoulder angle, θ1.4. Determine the wrist angle, θ3.17Multiple Solutions•The step for determining the elbow angle, θ2, may produce two solutions.•These are called the elbow up and elbow down configurations.18IK Modifications•The inverse kinematics calculations process described thus far is ideal for arms whose joints turn without bound and whose environments are obstacle free.•Modifications have been made to these calculations to create an IK solver specifically for the arm in this research.19IK Modifications•The joints cannot turn a full 360° because adjacent arm segments will collide.•The IK solver only uses configurations that are within the turning limits of each joint.20IK Modifications•Sometimes a target is not reachable from a desired orientation, but may be reached from another orientation.•The IK solver will search around the desired orientation at 10° intervals for 180° in both directions until a valid solution is found.21IK Modifications•When both elbow up and elbow