Chapter 10: Robot Control Systems:Joint Space Control and Task Space Control
- Perspective:Joint space control focuses on the robot's internal configuration (joint angles), while task space control focuses on the robot's external behavior (end-effector position and orientation).
- Implementation:
- Joint space control: Requires calculating the desired joint angles based on the desired task, often using inverse kinematics calculations.
- Task space control: Directly specifies the desired end-effector position and orientation, and the controller calculates the necessary joint angles to achieve it.
- Joint space control: Requires calculating the desired joint angles based on the desired task, often using inverse kinematics calculations.
- Intuitive Programming:Easier to program complex robot motions by specifying desired end-effector positions and orientations in the workspace, which is often more natural for users.
- Flexibility:Can handle changes in robot configuration or external environment without requiring major code modifications.
- Computational Complexity:Requires more complex calculations to convert desired task space positions into joint space commands, especially for robots with many degrees of freedom.
- Potential for Singularities:Certain robot configurations can lead to "singularities" where small changes in task space result in large joint angle changes, requiring careful control design.
- Joint Space Control:
- Simple robot motions where precise control of individual joints is needed.
- Situations where computational efficiency is critical.
- Task Space Control:
- Complex robot motions where the end-effector needs to follow a specific path in the workspace.
- User-friendly programming where specifying desired end-effector positions is more intuitive.
10.1 Introduction
Robot control systems play a crucial role in ensuring precise and efficient motion of robotic manipulators. These systems determine how a robot moves and interacts with its environment by controlling its actuators and joints. Two fundamental approaches to controlling robot manipulators are Joint Space Control and Task Space Control.
- Joint Space Control focuses on controlling the robot by specifying joint angles or joint velocities.
- Task Space Control directly controls the end-effector in Cartesian coordinates (position and orientation).
This chapter explores these two control paradigms, their mathematical formulation, and their applications in modern robotic systems.
10.2 Joint Space Control
10.2.1 Definition
In Joint Space Control, the robot's motion is planned and executed in terms of joint angles or joint velocities. Each joint is treated as an independent variable, and the robot is controlled by specifying desired joint positions, velocities, or torques.
10.2.2 Joint Space Representation
A robotic manipulator with degrees of freedom (DOF) is defined by a set of joint variables:
where represents the angle (for revolute joints) or displacement (for prismatic joints) of the joint.
The joint space trajectory is determined using kinematic and dynamic models of the robot.
10.2.3 Control Strategies in Joint Space
-
Proportional-Derivative (PD) Control
The simplest form of joint control is PD control, which ensures smooth motion and stability:where:
- is the control torque,
- and are proportional and derivative gains,
- and are desired joint positions and velocities,
- and are actual joint positions and velocities.
-
Computed Torque Control
This approach considers the robot dynamics using the equation of motion:where:
- is the inertia matrix,
- is the Coriolis/centrifugal matrix,
- is the gravity vector,
- is the control input.
The control law is defined as:
This method provides precise motion control but requires accurate dynamic modeling.
-
Adaptive Control
If the system parameters (e.g., mass, inertia) are uncertain, adaptive control is used to estimate and adjust the parameters dynamically.
10.3 Task Space Control
10.3.1 Definition
In Task Space Control, the robot’s motion is controlled in terms of the end-effector position and orientation rather than joint angles. This is useful when performing tasks such as pick-and-place, welding, or surgical operations, where precise Cartesian positioning is required.
10.3.2 Task Space Representation
The end-effector position and orientation are represented in a Cartesian frame as:
where define position, and define orientation. The mapping from joint space to task space is achieved using forward kinematics:
To control the motion in task space, the Jacobian matrix is used to relate joint velocities to end-effector velocities:
where is the Jacobian matrix.
10.3.3 Control Strategies in Task Space
-
Inverse Kinematics Control
The goal is to find the required joint angles for a desired end-effector position . This is done by solving the inverse kinematics equation:However, this approach can be complex for redundant or singular configurations.
-
Operational Space Control
This method directly controls forces and motions in task space using:where is the desired force/torque in task space, and maps it to joint torques.
-
Resolved Motion Rate Control
If the inverse kinematics is difficult to compute, the velocity-based approach is used:This ensures smooth trajectory tracking in task space.
10.4 Comparison of Joint Space and Task Space Control
| Feature | Joint Space Control | Task Space Control |
|---|---|---|
| Control Variables | Joint angles, velocities, torques | End-effector position, orientation |
| Suitability | Joint-level precision | Cartesian space tasks |
| Complexity | Easier to implement | Requires inverse kinematics |
| Applications | Industrial robots, manipulators | Surgical robots, teleoperation |
| Stability | More stable | Can be affected by kinematic singularities |
10.5 Applications in Robotics
- Industrial Robotics: Joint space control is commonly used for high-speed assembly and welding robots.
- Medical Robotics: Task space control is crucial in robotic surgery and rehabilitation devices.
- Humanoid Robots: A combination of both methods is used for complex movements.
- Teleoperation: Task space control is used for remotely operated robotic arms in hazardous environments.
10.6 Conclusion
Joint space control and task space control are fundamental approaches in robotics. While joint space control offers simplicity and direct control of actuators, task space control provides better precision for end-effector operations. Modern robotic systems often use a hybrid approach, combining the strengths of both methods. Understanding these control techniques is essential for designing advanced robotic applications.
References
- Spong, M. W., Hutchinson, S., & Vidyasagar, M. (2020). Robot Modeling and Control. Wiley.
- Siciliano, B., & Khatib, O. (2016). Springer Handbook of Robotics. Springer.
- Craig, J. J. (2018). Introduction to Robotics: Mechanics and Control. Pearson.
Comments
Post a Comment
"Thank you for seeking advice on your career journey! Our team is dedicated to providing personalized guidance on education and success. Please share your specific questions or concerns, and we'll assist you in navigating the path to a fulfilling and successful career."