Читать книгу Robot Modeling and Control - Mark W. Spong - Страница 6

1 Chapter 1Figure 1.1 A six-axis industrial manipulator, the KUKA 500 FORTEC robot. (Photo courtesy o...Figure 1.2 Estimated number of industrial robots worldwide 2014–2020. The industrial robot...Figure 1.3 Example of a typical mobile robot, the Fetch series. The figure on the right sh...Figure 1.4 Symbolic representation of robot joints. Each joint allows a single degree of f...Figure 1.5 The Kinova^® Gen3 Ultra lightweight arm, a 7-degree-of-freedom redundant manip...Figure 1.6 The integration of a mechanical arm, sensing, computation, user interface and t...Figure 1.7 Linear vs. rotational link motion showing that a smaller revolute joint can cov...Figure 1.8 The spherical wrist. The axes of rotation of the spherical wrist are typically ...Figure 1.9 A two-finger gripper. (Photo courtesy of Robotiq, Inc.)Figure 1.10 Anthropomorphic hand developed by Barrett Technologies. Such grippers allow for...Figure 1.11 Symbolic representation of an RRR manipulator (left), and the KUKA 500 arm (rig...Figure 1.12 Workspace of the elbow manipulator. The elbow manipulator provides a larger wor...Figure 1.13 Schematic representation of an RRP manipulator, referred to as a spherical robo...Figure 1.14 The ABB IRB910SC SCARA robot (left) and the symbolic representation showing a p...Figure 1.15 The ST Robotics R19 cylindrical robot (left) and the symbolic representation sh...Figure 1.16 The Yamaha YK-XC Cartesian robot (left) and the symbolic representation showing...Figure 1.17 The ABB IRB360 parallel robot. Parallel robots generally have higher structural...Figure 1.18 Two-link planar robot example. Each chapter of the text discusses a fundamental...Figure 1.19 Coordinate frames attached to the links of a two-link planar robot. Each coordi...Figure 1.20 A singular configuration results when the elbow is straight. In this configurat...Figure 1.21 The two-link elbow robot has two solutions to the inverse kinematics except at ...Figure 1.22 Solving for the joint angles of a two-link planar arm.Figure 1.23 Basic structure of a feedback control system. The compensator measures the erro...Figure 1.24 Diagram for Problem 1–12, 1–13, and 1–14.

2 Chapter 2Figure 2.1 Two coordinate frames, a point p, and two vectors v₁ and v₂.Figure 2.2 Coordinate frame o₁x₁y₁ is oriented at an angle θ with respect to ...Figure 2.3 Rotation about z₀ by an angle θ.Figure 2.4 Defining the relative orientation of two frames.Figure 2.5 Coordinate frame attached to a rigid body.Figure 2.6 The block in (b) is obtained by rotating the block in (a) by π about z₀.Figure 2.7 Rotating a vector about axis y₀.Figure 2.8 Composition of rotations about current axes.Figure 2.9 Composition of rotations about fixed axes.Figure 2.10 Euler angle representation.Figure 2.11 Roll, pitch, and yaw angles.Figure 2.12 Rotation about an arbitrary axis.Figure 2.13 Diagram for Problem 2–37.Figure 2.14 Diagram for Problem 2–38.

3 Chapter 3Figure 3.1 Coordinate frames attached to elbow manipulator.Figure 3.2 Coordinate frames satisfying assumptions DH1 and DH2.Figure 3.3 Positive sense for α_i and θ_i.Figure 3.4 Denavit–Hartenberg frame assignment.Figure 3.5 Tool frame assignment.Figure 3.6 Two-link planar manipulator. The z-axes all point out of the page, and are n...Figure 3.7 Three-link cylindrical manipulator.Figure 3.8 The spherical wrist frame assignment.Figure 3.9 Cylindrical robot with spherical wrist.Figure 3.10 DH coordinate frame assignment for the Stanford manipulator.Figure 3.11 DH coordinate frame assignment for the SCARA manipulator.Figure 3.12 Three-link planar arm of Problem 3–1.Figure 3.13 Two-link Cartesian robot of Problem 3–2.Figure 3.14 Two-link planar arm of Problem 3–3.Figure 3.15 Three-link planar arm with prismatic joint of Problem 3–4.Figure 3.16 Three-link articulated robot.Figure 3.17 Three-link Cartesian robot.Figure 3.18 Elbow manipulator with spherical wrist.Figure 3.19 Cartesian manipulator with spherical wrist.Figure 3.20 PUMA 260 manipulator.

4 Chapter 4Figure 4.1 Motion of the end effector due to prismatic joint i.Figure 4.2 Motion of the end effector due to revolute joint i.Figure 4.3 Finding the velocity of link 2 of a 3-link planar robot.Figure 4.4 Spherical wrist singularity.Figure 4.5 Elbow manipulator.Figure 4.6 Elbow singularities of the elbow manipulator.Figure 4.7 Singularity of the elbow manipulator with no offsets.Figure 4.8 Elbow manipulator with an offset at the elbow.Figure 4.9 Singularity of spherical manipulator with no offsets.Figure 4.10 SCARA manipulator singularity.Figure 4.11 Two-link planar robot.Figure 4.12 Manipulability ellipsoids are shown for several configurations of the two-link ...

5 Chapter 5Figure 5.1 Kinematic decoupling in the case of a spherical wrist. The vector oc is the...Figure 5.2 First three joints of a spherical manipulator.Figure 5.3 Singular configuration for a spherical manipulator in which the wrist center li...Figure 5.4 First three joints of an elbow manipulator.Figure 5.5 Singular configuration for an elbow manipulator in which the wrist center lies ...Figure 5.6 Elbow manipulator with shoulder offset.Figure 5.7 Left arm (left) and right arm (right) configurations for an elbow manipulator w...Figure 5.8 Projecting onto the plane formed by links 2 and 3.Figure 5.9 Four solutions of the inverse position kinematics for the PUMA manipulator.Figure 5.10 First three joints of a SCARA manipulator.Figure 5.11 Inverse kinematics solution using the Jacobian inverse. Desired end-effector co...Figure 5.12 Inverse kinematics solution using the Jacobian transpose. Desired end-effector ...Figure 5.13 Three-link planar robot with revolute joints.Figure 5.14 Three-link planar robot with prismatic joint.Figure 5.15 Cylindrical configuration.Figure 5.16 Cartesian configuration.

6 Chapter 6Figure 6.1 A particle of constant mass m constrained to move vertically constitutes a on...Figure 6.2 Single-link robot. The motor shaft is coupled to the axis of rotation of the li...Figure 6.3 Single-link, flexible-joint robot. The joint elasticity arises from flexibility...Figure 6.4 An unconstrained system of k particles has 3k degrees of freedom. If the pa...Figure 6.5 Examples of virtual displacements for a rigid bar. These infinitesimal motions ...Figure 6.6 A general rigid body has six degrees of freedom. The kinetic energy consists of...Figure 6.7 A rectangular solid with uniform mass density and coordinate frame attached at ...Figure 6.8 Two-link planar Cartesian robot. The orthogonal joint axes and linear joint mot...Figure 6.9 Two-link revolute joint arm. The rotational joint motion introduces dynamic cou...Figure 6.10 Two-link revolute joint arm with remotely driven link. Because of the remote dr...Figure 6.11 Generalized coordinates for the robot of Figure 6.10.Figure 6.12 Five-bar linkage.Figure 6.13 Forces and moments on link i

7 Chapter 7Figure 7.1 (a) The robot is a triangle-shaped rigid object in a two-dimensional workspace ...Figure 7.2 (a) The robot is a two-link planar arm and the workspace contains a single, sma...Figure 7.3 A graph with five vertices and six edges.Figure 7.4 This figure illustrates the construction of a free path using the visibility gr...Figure 7.5 A polygonal configuration space containing five obstacles, and its generalized ...Figure 7.6 A trapezoidal decomposition for the free configuration space for the case of po...Figure 7.7 In this case the gradient of the repulsive potential given by Equation (7.2) is...Figure 7.8 The configuration qi is a local minimum in the potential field. At qi t...Figure 7.9 The initial configuration for the two-link arm is given by θ₁ = θ₂ = 0 and ...Figure 7.10 The obstacle shown repels o₂, but is outside the distance of influence for ...Figure 7.11 The repulsive forces exerted on the origins of the DH frames o₁ and o₂ ...Figure 7.12 The two forces illustrated in the figure are vectors of equal magnitude in oppo...Figure 7.13 In this example, the robot is a polygon whose configuration can be represented ...Figure 7.14 The configuration q_min is a local minimum in the potential field. At qmi...Figure 7.15 This figures illustrates the steps in the construction of a probabilistic roadm...Figure 7.16 A new vertex is added to an existing tree by (i) generating a sample configurat...Figure 7.17 A typical joint space trajectory.Figure 7.18 (a) Cubic polynomial trajectory. (b) Velocity profile for cubic polynomial traj...Figure 7.19 (a) Quintic polynomial trajectory, (b) its velocity profile, and (c) its accele...Figure 7.20 Blend times for LSPB trajectory.Figure 7.21 (a) LSPB trajectory. (b) Velocity profile for LSPB trajectory. (c) Acceleration...Figure 7.22 (a) Minimum-time trajectory. (b) Velocity profile for minimum-time trajectory. ...Figure 7.23 (a) Cubic spline trajectory made from three cubic polynomials. (b) Velocity pro...Figure 7.24 (a) Trajectory with multiple quintic segments. (b) Velocity profile for multipl...

8 Chapter 8Figure 8.1 Basic structure of a feedback control system. The compensator measures the erro...Figure 8.2 Principle of operation of a permanent magnet DC motor. The magnitude of the for...Figure 8.3 Circuit diagram for an armature controlled DC motor. The rotor windings have an...Figure 8.4 Typical torque-speed curves of a DC motor. Each line represents the torque vers...Figure 8.5 Lumped model of a single link with actuator and gear train. Ja, Jg, and...Figure 8.6 Block diagram for a DC motor system. The block diagram represents a third-order...Figure 8.7 Block diagram for the reduced-order system. The block diagram now represents a ...Figure 8.8 Two-link manipulator with remotely driven link.Figure 8.9 Approximate range of effective inertias Jkk for the Stanford manipulator (...Figure 8.10 Block diagram of the simplified, open-loop system. The disturbance d/r repr...Figure 8.11 The system in Figure 8.10 with a PID compensator. KP, KI and KD are...Figure 8.12 The system in Figure 8.10 with a two-degree-of-freedom PID compensator.Figure 8.13 Second-order step responses with PD control. The speed of response, as measured...Figure 8.14 Second-order system with input saturation limiting the magnitude of the input s...Figure 8.15 Second-order step response with PD control and saturation.Figure 8.16 Response with integral control action showing that the steady-state error to a ...Figure 8.17 Feedforward control scheme. F(s) is the feedforward transfer function which...Figure 8.18 Feedforward control with disturbance D(s).Figure 8.19 Feedforward compensator for the second-order system of Section 8.5.Figure 8.20 Computed torque feedforward disturbance cancellation. The term (8.56) is added ...Figure 8.21 The Harmonic Drive^® gear. The rotation of the elliptical wave generator meshe...Figure 8.22 Idealized model to represent joint flexibility. The stiffness constant k repr...Figure 8.23 Block diagram for the system (8.59) and (8.60).Figure 8.24 PD control with motor angle feedback.Figure 8.25 PD control with load angle feedback.Figure 8.26 Step response — PD control with motor angle feedback (left) and with link angle...Figure 8.27 Root loci for the flexible joint systems. a) represents motor-angle feedback an...Figure 8.28 Coupled inertias in free space.

9 Chapter 9Figure 9.1 A single link of a flexible-joint manipulator. The joint elasticity is represen...Figure 9.2 Inner-loop/outer-loop control architecture. The inner-loop control computes the...Figure 9.3 The uniform ultimate boundedness set. Since is negative outside the ball B...Figure 9.4 Joint responses and input torques with saturated and unsaturated inverse dynami...Figure 9.5 Optimal joint trajectories and input torques using (9.128) compared with the un...Figure 9.6 Two-link RP manipulator.

10 Chapter 10Figure 10.1 A wrist force sensor. The array of strain gauges provides data of both force an...Figure 10.2 Robot end effector in contact with a rigid surface. The surface prevents motion...Figure 10.3 Inserting a peg into a hole, showing natural constraints imposed by the environ...Figure 10.4 The task of turning a crank with the resulting natural and artificial constrain...Figure 10.5 A robot in contact with a compliant environment. Both motion and force are perm...Figure 10.6 A one-port network can be thought of a black box representation of a system tha...Figure 10.7 Robot/environment interaction as an interconnection of one-port networks.Figure 10.8 Examples of (a) inertial, (b) resistive, and (c) capacitive environments.Figure 10.9 Thévenin (left) and Norton (right) equivalent networks.Figure 10.10 A mass M on a frictionless surface, subject to a force F.Figure 10.11 Capacitive environment case. The robot impedance is non-capacitive.Figure 10.12 Inertial environment case. The robot impedance is non-inertial.Figure 10.13 Two-link manipulator with remotely driven link.

11 Chapter 11Figure 11.1 The camera coordinate frame is placed at distance λ behind the image plane, w...Figure 11.2 Camera viewing a table from overhead, as in Example 11.8.Figure 11.3 The boundaries of the various sidewalks in this scene are all parallel, and the...Figure 11.4 The Sobel edge detector applies local image smoothing and a discrete approximat...Figure 11.5 The reference window is centered at (u₀, v₀), and the target window is ...Figure 11.6 The goal image is shown on the left. When the camera reaches the desired config...Figure 11.7 In (a) the desired feature point locations are shown in dark circles, and the i...Figure 11.8 The required camera motion is a rotation by π about the camera z-axis. In (...Figure 11.9 For the case of pure image-based control, each feature point would move on a st...Figure 11.10 The feature error trajectories for the motion illustrated in Figure 11.9, from ...

12 Chapter 12Figure 12.1 The sphere as a two-dimensional manifold in .Figure 12.2 Integral manifold in .Figure 12.3 Pictorial representation of a vector field on a manifold.Figure 12.4 Inner-loop/outer-loop control architecture for feedback linearization.Figure 12.5 Single-link, flexible joint robot.Figure 12.6 Step response and motor torque of the flexible joint robot. The difference betw...Figure 12.7 Tracking response and motor torque of the flexible joint robot with a cubic pol...Figure 12.8 Tracking response and motor torque of the flexible joint robot with an observer...

13 Chapter 13Figure 13.1 An underactuated serial-link robot.Figure 13.2 Upper-actuated (left) and lower-actuated (right) robots.Figure 13.3 Illustrating common reference angle conventions.Figure 13.4 The inverted pendulum on a cart.Figure 13.5 An overhead crane, a gimballed rocket and bipedal walking as examples of the in...Figure 13.6 The Acrobot as a gymnastic robot.Figure 13.7 The Pendubot.Figure 13.8 The Reaction-Wheel Pendulum.Figure 13.9 The Reaction Wheel Pendulum.Figure 13.10 Equilibrium configurations of the Acrobot and Pendubot under gravity with zero ...Figure 13.11 Local stabilization of the Reaction-Wheel Pendulum at the inverted position q...Figure 13.12 Equilibrium configurations of the Pendubot for ue nonzero.Figure 13.13 The determinant of the controllability matrix for equilibrium positions (0, π/2...Figure 13.14 Brachiation motion of the Acrobot with virtual holonomic constraint q₁ + 0....Figure 13.15 A simple pendulum with a force F acting at the bob.Figure 13.16 Phase portrait of the simple pendulum. The constant energy curves are solution ...Figure 13.17 Phase portrait of the closed-loop system. Figure generated by pplane, courtesy ...Figure 13.18 The Reaction-Wheel Pendulum as a parallel interconnection of passive systems.Figure 13.19 Swingup and balance of the Reaction-Wheel Pendulum (left) and phase plane traje...Figure 13.20 Reaction-wheel velocity (left) and saturated control input (right).Figure 13.21 Swingup and balance of the Acrobot using switching control

14 Chapter 14Figure 14.1 Mass m connected to a rigid rod.Figure 14.2 The rolling disk.Figure 14.3 The kinematic car.Figure 14.4 A hopping robot.Figure 14.5 The differential drive robot: top view (left), side view (right).Figure 14.6 The car parking problem.Figure 14.7 Illustrating the notion of Lie bracket direction.Figure 14.8 Response of z₁, z₂, and z₃: Note that z₁ and z₂ return to t...Figure 14.9 Response of z₁, z₂ and z₃.Figure 14.10 Trajectory and control inputs of the DDR computed from the flat outputs.Figure 14.11 Sliding-mode control of the DDR in chain form: response of the chain variables ...Figure 14.12 Sliding-mode control of the DDR in chain form: control inputs.Figure 14.13 Modified sliding-mode control of the DDR in chain form: response of the chain v...Figure 14.14 Modified sliding-mode control of the DDR in chain form: control inputs.Figure 14.15 DDR pose regulation.Figure 14.16 Differential drive robot showing the location of the output located d units a...Figure 14.17 Trajectory of the differential drive robot with partial feedback linearization ...

15 Appendix BFigure 1: The right hand rule.

16 Appendix CFigure C.1: Illustrating the definition of stability.