7.2 Robot Dynamics and Force Control
8 min read•july 30, 2024
Robot dynamics and force control are crucial for precise manipulation and interaction. They involve understanding how robots move and respond to forces, using mathematical models to describe their behavior.
These concepts are essential for designing control systems that enable robots to perform complex tasks. From assembly operations to collaborative applications, mastering dynamics and force control allows robots to work safely and efficiently in various industrial settings.
Dynamics of Robotic Manipulators
Lagrangian Formulation
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- The Lagrangian formulation derives the dynamic equations of motion for robotic manipulators using the difference between the kinetic and potential energy of the system
- The Lagrangian is defined as L = T - V, where T is the total kinetic energy and V is the total potential energy of the robotic manipulator
- The Euler-Lagrange equation, d/dt(∂L/∂q̇) - ∂L/∂q = τ, is used to derive the equations of motion
- q represents the joint positions and τ represents the joint torques
- The Lagrangian formulation considers the effects of , gravity, and external forces on the robotic manipulator's motion
- Example: A two-link planar robot arm can be modeled using the Lagrangian formulation to derive its dynamic equations of motion
Newton-Euler Formulation
- The Newton-Euler formulation derives the dynamic equations of motion by recursively computing the forces and torques acting on each link of the manipulator
- The Newton-Euler equations are based on Newton's second law of motion and Euler's equations for rotational motion
- The recursive algorithm propagates the velocities and accelerations from the base to the end-effector
- It then propagates the forces and torques back from the end-effector to the base
- The Newton-Euler formulation is computationally efficient and suitable for real-time control applications
- Example: A six-degree-of-freedom industrial robot's dynamics can be modeled using the Newton-Euler formulation for precise motion control
Joint Space and Cartesian Space Representations
- The dynamic equations of motion can be expressed in the joint space or the Cartesian space, depending on the control requirements and the task at hand
- Joint space representation describes the robot's dynamics in terms of joint positions, velocities, and torques
- Joint space control is suitable for tasks that require precise control of individual joint motions
- Example: Controlling a robotic arm's joint angles to follow a desired trajectory
- Cartesian space representation describes the robot's dynamics in terms of end-effector positions, velocities, and forces
- Cartesian space control is suitable for tasks that require precise control of the end-effector's motion and interaction with the environment
- Example: Controlling a robot's end-effector to draw a circle on a whiteboard
Force and Torque Control in Robots
Force Control Strategies
- Force control in robotics involves regulating the interaction forces between the robot and its environment to achieve desired contact behaviors and perform tasks that require precise force application
- is a force control strategy that regulates the dynamic relationship between the robot's motion and the interaction forces, allowing the robot to exhibit compliant behavior
- The impedance control law relates the desired impedance (, damping, and inertia) to the position and force errors
- Impedance control enables the robot to adapt its behavior based on the environmental constraints and the task requirements
- Example: A robotic gripper using impedance control to grasp fragile objects without causing damage
- Admittance control is a force control strategy that maps the measured interaction forces to desired position or velocity changes, allowing the robot to respond to external forces in a compliant manner
- Admittance control is the inverse of impedance control, as it relates the measured forces to the desired motion rather than the desired forces to the actual motion
- Example: A collaborative robot using admittance control to respond to human-applied forces and follow the human's lead
Hybrid Position/Force Control
- Hybrid position/force control is a strategy that decouples the task space into position-controlled and force-controlled subspaces, allowing simultaneous control of position and force in different directions
- The selection matrix is used to specify the directions in which position or force control is applied
- The position-controlled directions maintain precise position tracking
- The force-controlled directions regulate the interaction forces
- Hybrid control is suitable for tasks that require precise position control in some directions and force control in others
- Example: A robotic manipulator performing an assembly operation, where position control is used for alignment and force control is used for insertion
- Hybrid control enables the robot to adapt to environmental constraints while maintaining the desired position and force profiles
Inertia, Gravity, and Friction Effects
Inertial Effects
- Inertia refers to the resistance of a robotic manipulator to changes in its motion, which is determined by the and mass distribution of the robot's links
- The inertia matrix, denoted as M(q), is a symmetric positive definite matrix that captures the inertial properties of the robot and varies with the joint positions
- The inertia matrix appears in the dynamic equations of motion and affects the robot's acceleration and torque requirements
- The off-diagonal elements of the inertia matrix represent the coupling effects between the joints
- The inertial effects need to be considered in the control system design to ensure accurate and stable motion of the robotic manipulator
- Example: A heavy-duty industrial robot with large inertia requires higher torques to accelerate and decelerate its links compared to a lightweight collaborative robot
Gravitational Effects
- Gravity acts on the robotic manipulator, causing gravitational torques at the joints that depend on the robot's configuration and the orientation of the links with respect to the gravity vector
- The gravitational torque vector, denoted as G(q), is a function of the joint positions and can be computed using the potential energy of the system
- The gravitational torques tend to pull the robot towards a stable equilibrium configuration
- The gravitational effects are more pronounced in robots with long and heavy links
- Gravitational effects need to be compensated for in the control system to maintain the desired robot posture and motion
- Example: A robotic arm used for pick-and-place operations needs to compensate for the gravitational torques acting on its links to maintain precise positioning accuracy
Friction Effects
- Friction forces arise at the robot's joints and can significantly impact the robot's motion and control accuracy
- Coulomb friction is a constant friction force that opposes the direction of motion and is independent of the velocity magnitude
- Coulomb friction can cause stick-slip motion and limit the robot's ability to achieve smooth and precise movements
- Example: A robotic joint experiencing high Coulomb friction may exhibit jerky motion and reduced positioning accuracy
- Viscous friction is a velocity-dependent friction force that increases with the speed of motion
- Viscous friction dissipates energy and can cause the robot to slow down or overheat if not properly compensated for
- Example: A high-speed robotic manipulator may experience significant viscous friction, requiring additional torque to maintain the desired velocity
- Friction compensation techniques, such as model-based compensation or adaptive control, can be employed to mitigate the effects of friction on robot performance
Combined Effects and Control Challenges
- The combined effects of inertia, gravity, and friction contribute to the nonlinear and coupled dynamics of robotic manipulators, making their control and motion planning challenging
- The dynamic equations of motion need to account for these effects to accurately predict and control the robot's behavior
- Model-based control techniques, such as computed torque control, can be used to compensate for the nonlinear and coupled dynamics
- Adaptive control methods can be employed to estimate and compensate for unknown or time-varying parameters in the dynamic model
- The control system needs to be robust and responsive to handle the varying dynamics and external disturbances
- Example: A high-precision robotic surgery system needs to compensate for the combined effects of inertia, gravity, and friction to ensure accurate and stable motion of the surgical tools
Force Control Strategies for Robots
Assembly Operations
- Assembly operations require precise force control to ensure proper mating of parts and to prevent damage to the components
- Impedance control can be used to regulate the contact forces and accommodate position uncertainties during the assembly process
- The desired impedance parameters can be tuned to achieve the required stiffness and damping for different assembly tasks
- Example: A robotic manipulator using impedance control to insert a peg into a hole while maintaining the desired insertion force
- Force thresholds and trajectories can be defined to guide the robot in performing the assembly task while maintaining the desired force levels
- The force thresholds can be used to detect and respond to excessive or insufficient forces during the assembly process
- Example: A robotic gripper applying a specific force profile to snap two parts together without causing damage
Surface Following and Polishing
- Surface following and polishing tasks involve maintaining a constant contact force between the robot's end-effector and the target surface
- Hybrid position/force control can be employed to control the normal force perpendicular to the surface while allowing compliant motion in the tangential directions
- The position-controlled directions ensure accurate tracking of the surface contour
- The force-controlled direction maintains the desired contact force for consistent polishing or surface treatment
- Force feedback from sensors mounted on the end-effector can be used to adjust the robot's motion and maintain the desired contact force
- The force feedback can be used in a system to compensate for surface irregularities and variations in material properties
- Example: A robotic polishing system using force feedback to maintain a constant polishing pressure on a curved surface
Collaborative Robot Applications
- Collaborative robot applications, where robots work alongside humans, require safe and responsive force control to prevent injuries and ensure smooth interactions
- Admittance control can be implemented to enable the robot to react to human-applied forces and adapt its motion accordingly
- The admittance control parameters can be tuned to achieve the desired level of responsiveness and
- Example: A collaborative robot using admittance control to assist a human operator in a shared task, such as lifting and moving heavy objects
- Force and torque limits can be set to ensure that the robot operates within safe boundaries and can detect and respond to unexpected collisions or disturbances
- The force and torque limits can be based on safety standards and risk assessments for collaborative robot applications
- Example: A collaborative robot with force and torque limits that trigger an emergency stop if the limits are exceeded during human-robot interaction
Robotic Surgery
- Robotic surgery demands high precision and delicate force control to perform surgical procedures accurately and minimize tissue damage
- Impedance control strategies can be tailored to provide the desired stiffness and damping characteristics for different surgical tools and tasks
- The impedance parameters can be adjusted based on the specific surgical procedure and the properties of the target tissues
- Example: A robotic surgical system using impedance control to limit the force applied by a cutting tool to prevent excessive tissue damage
- Haptic feedback can be incorporated to provide the surgeon with a sense of touch and improve the control and safety of the surgical procedure
- Haptic feedback can convey information about the interaction forces between the surgical tools and the patient's anatomy
- Example: A robotic surgery system providing haptic feedback to the surgeon to indicate the presence of hard or soft tissues during a dissection task
Key Terms to Review (17)
Closed-loop control: Closed-loop control is a system where the output is continuously monitored and compared to a desired setpoint, allowing for automatic adjustments to be made based on the difference between the actual output and the target. This feedback mechanism is crucial for maintaining accuracy and stability in various applications, ensuring systems respond dynamically to changes and disturbances.
Compliance: Compliance refers to the ability of a system or component to deform or yield under an applied force while maintaining its overall integrity. In the context of robotics, compliance is crucial for enabling safe and effective interaction between robots and their environment, especially during force control tasks where precision and adaptability are necessary.
Coriolis Force: Coriolis force is an apparent force that acts on objects moving within a rotating frame of reference, causing them to deviate from their original path. This phenomenon is crucial in robot dynamics and force control, as it affects the motion of robots operating in a rotating environment and must be accounted for when calculating trajectories and forces.
Force Control Loop: A force control loop is a feedback system used in robotics and automation to regulate the forces exerted by a robot's end effector during interaction with objects or environments. This control loop continuously measures the forces and adjusts the robot's actions in real-time to maintain desired force levels, which is crucial for tasks requiring precision, such as assembly or delicate manipulation. By integrating sensors and actuators, the force control loop enhances the robot's performance in dynamic and uncertain environments.
Force-torque sensor: A force-torque sensor is a device that measures the forces and moments acting on an object, typically used in robotics to provide feedback for motion control and interaction with the environment. These sensors enable robots to detect contact forces, ensuring safe and precise manipulation of objects while performing tasks like assembly or handling. By integrating these measurements into control algorithms, robots can achieve improved performance in dynamic environments.
Forward kinematics: Forward kinematics is the process of calculating the position and orientation of a robotic end-effector based on the given joint parameters or configurations. It is essential in understanding how a robot moves and interacts with its environment, as it allows for the determination of the robot's pose in Cartesian space from its joint angles. This concept is foundational for tasks involving motion planning, control, and analysis of robotic systems.
Gravitational Force: Gravitational force is the attractive force that exists between any two masses due to their mass and distance apart. This fundamental force plays a crucial role in robot dynamics, influencing the motion and stability of robotic systems, especially when considering the interaction between the robot and its environment. Understanding gravitational force is essential for accurately modeling robot behavior under various conditions and developing effective force control strategies.
Impedance Control: Impedance control is a technique used in robotics that regulates the dynamic relationship between the motion of a robot and the external forces it experiences. It allows robots to adaptively adjust their compliance, or stiffness, in response to external disturbances, making them better suited for tasks that require interaction with uncertain environments. This concept is crucial in achieving effective force control, enabling robots to maintain stability while executing tasks that involve physical interaction.
Inertia: Inertia is the property of matter that describes its resistance to changes in motion. This fundamental concept explains how an object at rest tends to stay at rest and an object in motion continues in its state of motion unless acted upon by an external force. In the context of robotic systems, understanding inertia is crucial for predicting how robots will behave during movement and how to effectively control forces during interactions with their environment.
Inverse kinematics: Inverse kinematics is a mathematical process used to determine the joint angles and positions needed for a robotic arm or mechanism to achieve a desired end-effector position and orientation. This process is essential for tasks like programming robots, controlling their dynamics, planning their motions, and understanding their kinematic behaviors in various coordinate systems.
Kinematics: Kinematics is the branch of mechanics that focuses on the motion of objects without considering the forces that cause this motion. It is essential for understanding how robots and mechanical systems move, as it involves concepts like position, velocity, and acceleration. Kinematics provides the mathematical framework necessary to analyze movement, which is crucial when integrating robotic systems into broader mechatronic applications.
Lagrange Equations: Lagrange equations are a set of second-order differential equations used to describe the dynamics of a mechanical system. They are derived from the principle of least action and are essential in formulating the equations of motion for systems with generalized coordinates, making them particularly useful in robot dynamics and force control.
Load Cell: A load cell is a type of transducer that converts a force or load into an electrical signal, often used in weighing systems. This device is crucial for measuring weight, pressure, and force, allowing for accurate feedback in robotic systems. By providing precise measurements of the forces exerted during operation, load cells play an essential role in maintaining control and stability in robot dynamics and force control applications.
Mass: Mass is a measure of the amount of matter in an object, typically expressed in kilograms or grams. In the context of robot dynamics and force control, mass plays a crucial role in determining the inertial properties of a robotic system, influencing how robots move and interact with their environment. It affects the robot's acceleration, stability, and overall performance when executing tasks.
Newton's Laws of Motion: Newton's Laws of Motion are three fundamental principles that describe the relationship between the motion of an object and the forces acting on it. These laws form the foundation of classical mechanics and are essential for understanding how robots move and interact with their environment, especially in terms of dynamics and force control.
Open-loop control: Open-loop control is a type of control system that operates without using feedback to determine if the output has achieved the desired effect. This means that once the input command is given, the system executes its operations based solely on pre-set conditions, without adjusting based on the actual output or external factors. This approach is often simpler and less costly, but it can lead to inaccuracies and inefficiencies if external conditions change or if there are disturbances in the system.
Stiffness: Stiffness is a measure of a material's resistance to deformation when a force is applied. In the context of robotics, stiffness plays a critical role in determining how robots interact with their environment and how they can maintain precision in movement while applying or resisting forces. The relationship between stiffness and dynamics affects a robot's ability to perform tasks accurately, maintain stability, and control force exertion.