Mark W. Spong - Robot Modeling and Control

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 3 k 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 θ 1= θ 2= 0 and ...Figure 7.10 The obstacle shown repels o 2, but is outside the distance of influence for ...Figure 7.11 The repulsive forces exerted on the origins of the DH frames o 1and o 2...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 minis a local minimum in the potential field. At q mi...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 ( u 0, v 0), 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 ...