Robot System Modeling

Abstract

Robot system modeling is the foundation for verifying a robot’s motion control and simulation. The 3D robot model in ROS is implemented through a Unified Robot Description Format (URDF) file, which is an XML file describing the robot as well as its parts structure, joints, and degrees of freedom (DOF). The 3D robot in the ROS system has a corresponding URDF file. This chapter covers several common-wheeled robot motion models and robot modeling with URDF. The robot motion control is performed through ROS to achieve synchronized motion between the simulated and real robots. Then, the typical sensor in robot systems, light detection and ranging (LiDAR), is discussed. Finally, readers can observe the scene profile point cloud data to experience environment sensing and obstacle detection from the robot’s perspective.

Appendices

Further Reading

The concept of redundancy of robot manipulator is relative and defined for specific tasks. For a flat task, the commonly used 6-axis (six-degree-of-freedom) robot manipulator is also redundant. However, it is common practice to generalize this concept for all tasks, as three-dimensional space can be described in terms of six degrees of freedom. Consequently, a 7-axis (seven degree-of-freedom) manipulator is often referred to as a redundant robot manipulator.

We can use the extra degrees of freedom of redundant robot manipulator to achieve additional tasks such as ontology obstacle avoidance, singularity avoidance, joint limit avoidance, joint torque optimization, and increasing the degree of operation. At the same time, since one arm of a human also has seven degrees of freedom, from the perspective of bionics, redundant arms are also more realistic.

An S-R-S type anthropomorphic manipulator comprises a relatively simple structure, similar to that of the human arm. As shown in Fig. 3.32, the manipulator is composed of seven revolute joints. The first three and the last three joints can be regarded as equivalent spherical joints because their axes intersect at a single point. The spherical joints will be referred to as shoulder (S) and wrist (W) joint, respectively, in analogy to those of the human arm. In a similar way, the middle joint (Joint #4) will be called the elbow (E) joint. Furthermore, similar to the human arm, the S-R-S type manipulator comprises two characteristic subchains¹: the positioning subchain formed by the first four joints with coordinates q_i, i = 1, 2, 3, 4, and the orientation subchain formed by the last three (wrist) joints with coordinates q_j, j = 5, 6, 7.

Fig. 3.32

Kinematic structure of S-R-S type manipulator

An analytical methodology has been proposed for obtaining all of the feasible inverse kinematic solutions for a S-R-S redundant manipulator in the global configuration space constrained by joint limits². The method could also be applied to the redundancy resolution problem. Firstly, a parameterized inverse kinematic solution was derived using the arm angle parameter. Then, the relations between the arm angle and joint angles were investigated in detail, and how to obtain feasible inverse solutions satisfying joint limits was discussed. Finally, the inverse kinematic computation method was applied to the redundancy resolution problem. Analytical methods for joint limit avoidance were also developed.

The S-R-S inverse kinematics simulation based on MATLAB can refer to the network link³.

Exercises

• 1. It is known that the wheel radius of a differentially driven mobile robot is r, the distance from the driving wheel to the middle point P of the two wheels is d, and the rotational angular velocities of the left wheel and the right wheel are ${\dot{\varphi}}_1,{\dot{\varphi}}_2$, respectively. Place the robot in the planar global coordinate system, in which and the posture is expressed as ξ_I = (x, y, θ)^T. How to calculate its kinematic model ξ ̇_I, which is also shown as ${\left(\dot{x},\dot{y},\dot{\theta}\right)}^T$.

• 2. How to load the world model in Gazebo via roslaunch? And how to add a URDF model to Gazebo via roslaunch?

• 3. How to create a 0.6 × 0.1 0.2 white cube URDF model.

• 4. How to set up the view model, collision model, and inertia model for link in the URDF file?

• 5. In the URDF file, use x, y, and z to indicate the displacement offset in the direction of the x − axis, y − axis, and z − axis, respectively (units: m); r, p, and y indicate the rotation around the x-axis, y-axis, and z-axis, and amount, respectively (units: rad). Given that x = 0.25, y = 0.24, z = 0.8, r = PI/2, r = PI/6, r =  − PI/4, to solve the rotation matrix, translation matrix and quaternion representation of the transformation relationship.

• 6. For the Ackermann-driven type whose chassis motion characteristics of the wheeled robot are front-wheel steering and rear-wheel drive, how to obtain the inverse kinematics equation?

• 7. What is the message format of the LiDAR message type sensor_msgs/LaserScan?

• 8. Referring to Figs. 1.4 and 1.5 (demonstrates the two-wheeled differential motion model in Chap. 1), to analyze the odometer model of the two-wheeled differential robot.