12.1 Robot manipulator control
2 min read•july 25, 2024
Robot manipulators are complex machines that require precise control. Understanding their dynamics and kinematics is crucial for effective operation. This includes forward and inverse kinematics, velocity kinematics, and dynamics modeling using methods like Lagrangian or Newton-Euler formulations.
Adaptive control techniques help robots handle varying conditions. Methods like and adjust controller parameters on the fly. Advanced techniques like force control and performance evaluation ensure robots can interact safely with their environment and operate efficiently.
Robot Manipulator Dynamics and Control
Dynamics and kinematics of manipulators
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- Forward kinematics maps joint angles to end-effector position using DH parameters and homogeneous transformation matrices
- Inverse kinematics determines joint angles for desired end-effector position through analytical or numerical methods (Newton-Raphson)
- Velocity kinematics relates joint velocities to end-effector velocity using Jacobian matrix identifies singularities
- Dynamics modeling derives equations of motion via Lagrangian or Newton-Euler formulations
- Equations of motion include inertia matrix, Coriolis and centrifugal terms, and gravity terms
- Actuator dynamics consider motor characteristics and gear transmission effects
Adaptive control for varying conditions
- Model reference adaptive control (MRAC) uses reference model and adaptation laws to adjust controller parameters
- Self-tuning regulators (STR) employ parameter estimation techniques and control law design for online adaptation
- performs online parameter estimation and adaptive feedforward compensation
- incorporates sliding mode control or control for improved
- utilize (RLS) or for real-time mass estimation
Advanced Control Techniques and Performance Evaluation
Force control in environmental contact
- defines desired impedance model and uses force feedback for compliant interaction
- specifies desired admittance model and utilizes position/velocity feedback
- employs task frame formulation to separate force and position subspaces
- manipulates Cartesian stiffness matrix and joint space stiffness for desired behavior
- Contact modeling considers rigid body contact or compliant contact models for accurate interaction simulation
Performance evaluation of adaptive algorithms
- Performance metrics assess , , and
- Stability analysis applies theory and input-to-state stability concepts
- Robustness analysis examines controller behavior under parameter variations and external disturbances
- Simulation tools like and enable virtual testing and validation
- Experimental setup integrates sensors (encoders, force/torque sensors) and implements real-time control
- Comparative analysis evaluates adaptive vs. non-adaptive control and different adaptive control schemes
Key Terms to Review (20)
Adaptive computed torque control: Adaptive computed torque control is a method used in robot manipulator control that adjusts the control input based on the estimated parameters of the robot's dynamics. This approach aims to compensate for uncertainties and variations in the system, ensuring accurate tracking of desired trajectories while maintaining stability. By dynamically updating the control law, it effectively improves performance in real-time applications, making it particularly useful in environments where model parameters may change.
Admittance Control: Admittance control is a control strategy used in robotics where the system's input is based on the desired motion and the external forces acting on the robot. This approach allows robots to interact more safely and effectively with their environment by adapting their behavior according to the external forces they encounter. It emphasizes the importance of dynamic interaction, enabling smoother and more responsive manipulation tasks while maintaining stability.
H. F. Durrant-Whyte: H. F. Durrant-Whyte is a prominent researcher in the field of robotics and control systems, known for his contributions to robot manipulator control and sensor-based systems. His work often emphasizes the importance of adaptive control techniques, allowing robots to improve their performance through learning and environmental interaction. Durrant-Whyte's research has influenced the development of various algorithms that enhance the efficiency and effectiveness of robotic systems in real-world applications.
Hybrid position/force control: Hybrid position/force control is a control strategy that enables a robotic system to simultaneously manage both the position of the end effector and the force exerted on an object it interacts with. This method allows for versatile manipulation in tasks where the robot must adhere to specific positions while also applying the right amount of force, making it crucial in applications such as assembly, handling delicate objects, and human-robot interaction.
Impedance Control: Impedance control is a control strategy used in robotics that allows a manipulator to interact with its environment in a compliant manner. By regulating the dynamic relationship between the applied forces and the resulting motion, impedance control enables robots to adapt their stiffness and damping properties, facilitating safe and effective physical interaction with objects and surfaces during tasks.
Kalman Filtering: Kalman filtering is a mathematical technique used for estimating the state of a dynamic system from a series of noisy measurements. It provides an efficient recursive solution to the linear quadratic estimation problem, enabling the continuous updating of state estimates based on new incoming data. This method is particularly valuable in real-time applications, where it enhances the accuracy of measurements and system performance, making it essential in online identification and control processes, as well as in robotic systems for motion tracking and control.
Lyapunov Stability: Lyapunov stability refers to a concept in control theory that assesses the stability of dynamical systems based on the behavior of their trajectories in relation to an equilibrium point. Essentially, a system is considered Lyapunov stable if, when perturbed slightly, it returns to its original state over time, indicating that the equilibrium point is attractive and robust against small disturbances.
Matlab/simulink: MATLAB/Simulink is a high-level programming environment and simulation tool designed for mathematical computations, algorithm development, data analysis, and system modeling. This platform is extensively used in engineering and scientific research for its powerful visualization capabilities and the ability to model complex systems through simulations. With features that support control system design, it allows users to implement adaptive and self-tuning control strategies, making it an essential tool in modern control theory applications.
Model Reference Adaptive Control: Model Reference Adaptive Control (MRAC) is a type of adaptive control strategy that adjusts the controller parameters in real-time to ensure that the output of a controlled system follows the behavior of a reference model. This approach is designed to handle uncertainties and changes in system dynamics, making it particularly useful in applications where the system characteristics are not precisely known or may change over time.
Overshoot: Overshoot refers to the phenomenon where a system exceeds its desired final output or steady-state value during transient response before settling down. This characteristic is significant in control systems, as it affects stability, performance, and how quickly a system can respond to changes.
Payload estimation techniques: Payload estimation techniques are methods used to estimate the weight and characteristics of the payload being carried by a robotic manipulator. These techniques are essential for ensuring that the manipulator can effectively manage the loads it is handling, maintaining stability, safety, and efficiency during operation. Accurate payload estimation allows for better control strategies and performance optimization of robotic systems.
Recursive Least Squares: Recursive least squares (RLS) is an adaptive filtering algorithm that recursively minimizes the least squares cost function to estimate the parameters of a system in real-time. It allows for the continuous update of parameter estimates as new data becomes available, making it highly effective for dynamic systems where conditions change over time.
Robust Adaptive Control: Robust adaptive control is a control strategy that adjusts itself in real-time to manage uncertainty and variations in system dynamics while maintaining performance stability. This approach combines the principles of robustness, which ensures stability against disturbances and model inaccuracies, with adaptive control, which allows systems to learn and modify their control actions based on changing conditions.
Robustness: Robustness refers to the ability of a control system to maintain performance despite uncertainties, disturbances, or variations in system parameters. It is a crucial quality that ensures stability and reliability across diverse operating conditions, enabling the system to adapt effectively and continue functioning as intended.
Ros/gazebo: ROS (Robot Operating System) is an open-source framework that provides libraries and tools to help software developers create robot applications. Gazebo is a simulation environment that integrates with ROS, allowing users to simulate complex robotic systems in a 3D environment. Together, they enable developers to design, test, and visualize robot behaviors and control strategies without the need for physical hardware.
Self-Tuning Regulators: Self-tuning regulators are adaptive control systems that automatically adjust their parameters based on real-time measurements of the system’s output and behavior. This ability to adapt in real-time allows them to maintain performance despite changes in system dynamics or external disturbances, making them a powerful tool in various applications.
Settling Time: Settling time is the duration required for a system's output to reach and remain within a specified range of the final value after a disturbance or a change in input. This concept is essential for assessing the speed and stability of control systems, particularly in how quickly they can respond to changes and settle into a steady state.
Shankar Sastry: Shankar Sastry is a prominent figure in the field of adaptive and self-tuning control, known for his contributions to the theory and application of control systems. His work emphasizes the integration of learning algorithms into control frameworks, leading to significant advancements in adaptive control strategies, particularly in robotic applications and systems that require real-time adjustments to dynamic environments.
Stiffness Control: Stiffness control refers to a technique used in the control of robotic manipulators to regulate the rigidity or compliance of the robot's end effector. This approach is essential for ensuring precise interactions with the environment, particularly when dealing with tasks that require delicate manipulation or contact with uncertain surfaces. By adjusting stiffness dynamically, robots can adapt their behavior based on external forces, enhancing performance in tasks like assembly, painting, or surgery.
Tracking error: Tracking error is the deviation between the actual output of a control system and the desired output, typically expressed as a measure of performance in adaptive control systems. This concept is crucial in evaluating how well a control system can follow a reference trajectory or setpoint over time, and it highlights the system's ability to adapt to changes in the environment or internal dynamics.