A Mathematical Introduction to Robotic Manipulation

Presents a slightly more abstract (mathematical) formulation of the kinematics, dynamics, and control of robot manipulators. DLC: Robotics.To Ruth Anne(RMMJianghua(∠XLIn memory of my father(SSS)ContentsContentsPrefaceAcknowledgementsⅹV111 Introduction1 Brief hist2 Multifingered Hands and Dextrous Manipulation3 Outlinc of the book133.1Ming single roL143.2 Coordinated manipulation using multifingered robothand3.3 NonholOnIOnnic behavior ill robotic systeNs164Bibliography182 Rigid Body Motion192 Rotational Motion in p. ons1 Rigid body Transformatic222.1 Properties of rotation matrices232.2 Exponential coordinates for rotation272.3 Other representations313 Rigid motion in r3343. 1 Homogeneous representation363.2 Exponentia l coordinates for rigid motion and twist s 393.3 Screws: a geometric description of twists454 Velocity of a Rigid Body514.1 Rotational velc514Rigid body vclocity4.3 Velocity of a screw motion574.4 Coordinate transformations85 Wrenches and Reciprocal Screws615.1615.2 Screw coordinates for a wrench5.3 Reciprocal screws666 Summary7 Biblgraphy8 E3 Manipulator Kinematics811 Introduction81Forward Kincmatics2.1 Proble statement2.2 The product of exponentia ls formula2.3 Parameterization of manipulators via twists2.4 Manipulator workspace953 Inverse kinematics3.1planar example973.2 Paden-Kahan subproblems93.3 Solving inverse kinematics using subproblems1043.4 General solutions to inverse kinematics problems 1084 The Manipulator Jacobian1154.1 End-effector velocity1154.2 End-effector forces1214.3 Singularities1234.4 Manipulability5 Redundant and Parallel Manipulators5.1 Redundant manipulators1295.2 Parallel manipulators1325.3 Four-bar linkage1355.4 Stewart platform1386 Summary1437 Bibliography1448 Exercises.1464 Robot Dynamics and Control1551 Introduction1552 Lagrange' s Equations1562.1 Basic formulation2.2 Inertial properties of rigid bodies2.3 Example: Dynamics of a two-link planar robot .. 1642.4 Newton-Euler equations for a rigid body1653 Dynamics of Open-Chain Manipulators1683. 1 The Lagrangian for an open-chain robot1683.2 Equations of motion for an open-chain manipulator 1693.3 Robot dynamics and the product of exponentialsformula鲁鲁4 Lyapunov Stability Theory1794.1 Basic definitions4.2 The direct method of Lyapunov1814.3 Thc indirect mcthod of lyapunov1844.4 Examples1854.5Lasalle, s invariance principle5 Position Control and Trajectory Tracking1895.1 Problem description905.2 Computed torque5.3 PD control5.4 Workspace control1956 Control of Constrained manipulators26.1 Dynamics of constrained systems2006.2 Control of constrained manipulato2016.3 Example: A planar manipulator moving in a slot. 203Summary2068 Bibliography2079 Exercises2085 Multifingered Hand Kinematics2111 Introduction to Grasping2112 Grasp statics2142.1 Contact models.2142.2e grasp2183上orce- Closure)5)3.1 Formal definition2233.2 Constructive force-closure conditions4 Grasp Planning2294.1 Bounds on number of required contacts4.2 Constructing force-closure grasps2325 Grasp Constraints5.1 Finger kinematics2345.2 Properties of a multifingered grasp5.3 Fxample: Two SCARA fingers grasping a box2406 Rolling contact Kinematics2426.1 Surface models2436.2 Contact kinematics2486.3 Grasp kinematics with rolling2537 Summary.256Bibliography9 Exercises2596 Hand Dynamics and Control2651 Lagrange's Equations with Constraints2651.1 Pfaffian constraints21. 2 Lagrange multipliers2691.3 Lagrange-d'Alembert formulation1.4 The nature of nonholonomic constraints274e Robot Hand dynamics2762.1 Derivation and properties2762.2 Internal forces2792.3 Other robot systems.2813 Redundant and Nonmanipulable Robot Systems283.1 Dynamics of redundant manipulators2863.22903.3 Example: I wo-fingered Scara grasp04 Kinematics and Statics of Tendon Actuation2934.1 Inelastic tendons2944.2 Elastic tendons294.3 Analysis and control of tendon-driven fingers2985 Control of robot hands3005.1 Extending controllers3005.2 Hierarchical control structurcs3026 Summary3117 Bibliography.313E3147 Nonholonomic Behavior in Robotic Systems3171 Introductio3172 Controllability and Frobenius'Theorem.3212.1 Vector fields and flows3222.2 Lie brackets and Frobenius' theorem3232.3 Nonlinear controllability3283 Examples of Nonholonomic Systems3324 Structure of Nonholonomic SysteIIs4. Classification of nonholonomic distributions344.2 Examples of nonholonomic systems, continued3414.3 Philip lall basis3445 Summary3466 Bibliography3477 Exercises3498 Nonholonomic Motion Planning3551 Introduction355Steering Model Control Systems Using Sinusoids3582.1 First-order controllable systeMs: Brockett's systeIll 3582.2Second-order controllable svstems3612.3 Higher-order systems: chained form systems.... 363 General Methods for Steering3663.1 Fourier techniques3673.2 Conversion to chained form3693.3 Optimal steering of nonholonomic systems3.4 Steering with piecewise COnistant inputs3754 Dynamic Finger Repositioning384.1 Problcm description3824.2 Steering using sinusoids3834.3 Geometric phase algorith3855 Summary3896 Bibliography3907 Exercises3919 Future Prospects3951 Robots in Hazardous Environments3962 Medical Applications for Multifingered Ilands3983 Robots on a small scale: Microrobotics399a Lie Groups and robot Kinematics403Lic groups and robot Kincmatics4031 Differentiable manifolds4031.1 Manifolds and maps4031.2 Tangent spaces and tangent maps4041.3 Cotangent spaces and cotangent maps4051.4 Vector fields4061.5 Differential forms4082 Lie groups4082.1 Definition and exalnples4082.2 The Lie algebra associated with a lie group402.3 Thc exponential map412.4 Canonical coordinates on a Lie group4142.5 Actions of Lie g4153 The Geometry of the Euclidean Group4163.1 Basic properties4163.2 Metric properties of SE(3)4223.3 Volume forms on SE()430B A Mathematica Package for Screw Calculus435Bibliography441Iudex449X11