CONTROL STRATEGIES AND

ADVANCED ROBOTICS
 C O N T R O L L E R D E S I G N U S I N G T H E C O M P U T E D T O R Q U E M E T H O D

Computed Torque Control (CTC) is a sophisticated approach to controlling robotic arms. Imagine you have a robot with multiple joints, and you
want to make it moves precisely along a specific path. However, the dynamics governing the robot's motion are complex and nonlinear. CTC
simplifies this complexity by using the inverse dynamics of the robot. It essentially calculates the forces or torques needed at each joint to
counteract the inherent nonlinearities in the robot's movement. By doing this, CTC linearizes and separates the complex dynamics, making it
easier to control the robot accurately.
Key Steps in CTC:
• Derive the Inverse Dynamics: Calculate the inverse dynamics of the manipulator, which expresses the desired joint torques required to
achieve a desired joint acceleration.
• What It Is: Figure out a rule that tells us how much force or push each joint in the robot needs to move in a certain way.

• Why It's Important: This rule (inverse dynamics) helps us understand how the robot responds to forces and accelerates.

• Feedforward Control: Apply the inverse dynamics as feedforward control to compensate for the nonlinear dynamics.
• What It Is: Use the rule we figured out to calculate the initial forces needed to make the robot move according to our plan.
• Why It's Important: This step sets the basic forces required to follow the desired motion without considering external influences.

• Feedback Control: Design a feedback controller to deal with uncertainties and disturbances.
• What It Is: Keep an eye on how well the robot is actually moving and adjust the forces in real-time based on what we see.

• Why It's Important: This adjustment ensures that the robot stays on track even if there are unexpected factors or changes in its environment.
 C O N T R O L L E R D E S I G N U S I N G T H E C O M P U T E D T O R Q U E M E T H O D

• Basically

Step 1: Figure out how hard each joint should push to move as we want.
• Step 2: Use that knowledge to start moving, considering only our original plan.
• Step 3: Keep watching and adjusting in case something unexpected happens, so the robot stays on course.

Advantages of CTC:

• CTC takes the intricate movements of a robotic arm and makes them act more predictably, like simple linear motions. It separates the movements of different joints, making it easier to
control one thing at a time. This simplification makes it much more manageable for humans (or controllers) to guide the robot along desired paths accurately.

• Achieves high precision and tracking performance

• Robust to parameter uncertainties

Disadvantages of CTC:
• Requires accurate knowledge of manipulator dynamics
• Computational complexity can be high for complex manipulators
• Sensitive to actuator noise and disturbances
 C O N T RO L L E R D ES I G N U S I N G T H E C O MP U T E D TO RQ U E ME T H O D

A robotic arm (shoulder and elbow joints) that you want to control to follow a circular trajectory. The goal is to design a controller using the computed torque method to make the robot move
in a smooth and precise circular path.

Dynamic Model:
• Begin with the dynamic model of the robot, which describes how the robot's joints respond to external forces and torques. The dynamic model is typically represented as an equation of motion, such as:
M(q)q¨+C(q,q˙)q˙+G(q)=τM(q)q¨​+C(q,q˙​)q˙​+G(q)=τ

• M(q)M(q) is the inertia matrix, C(q,q˙)C(q,q˙​) includes Coriolis and centrifugal terms, G(q)G(q) is the gravity vector, q¨q¨​is the joint acceleration, q˙q˙​is the joint velocity, and ττ is the joint torque.

Inverse Dynamics:
• Solve the dynamic equation for q¨q¨​to obtain the inverse dynamics. This step involves expressing the joint accelerations in terms of the joint torques: q¨=M(q)−1( τ−C(q,q˙)q˙−G(q))q¨​=M(q)−1(τ−C(q,q˙​
)q˙​−G(q))

Desired Trajectory:
• Define a desired trajectory for the robot, specifying the desired joint positions, velocities, and accelerations over time.

Feedforward Control:
• Calculate the feedforward torques needed to follow the desired trajectory by applying the inverse dynamics: τfeedforward=M(q)q¨desiredτfeedforward​=M(q)q¨​desired​

• This represents the initial torques required to achieve the desired joint accelerations.

Feedback Control (Optional):

• If feedback control is included, measure the actual joint positions, velocities, and accelerations during robot operation.

• Calculate the tracking error by comparing the actual and desired joint states: e=qdesired−q e=qdesired​−q, e˙=q˙desired−q˙e˙=q˙​desired​−q˙​.

• Apply feedback control to adjust the torques based on the tracking error: τfeedback=Kpe+Kde˙τfeedback​=Kp​e+Kd​e˙

• The total control torques become: τtotal=τfeedforward+τfeedbackτtotal​=τfeedforward​+τfeedback​.

Actuation:
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CONTROLLER DESIGN USING THE
COMPUTED TORQUE METHOD
 C L A S S I C A L C O N T R O L S T R AT E G I E S F O R M A N I P U L AT O R S A N D M O B I L E R O B O T S

Classical control strategies are well-established methods for controlling robotic systems. They are often preferred due to their
simplicity, effectiveness, and robustness.

Common Classical Control Strategies:

• Proportional (P) control: Provides a control signal proportional to the error.
• Integral (I) control: Eliminates steady-state error by accumulating the error over time.
• Derivative (D) control: Dumps oscillations by reacting to the rate of change of error.
• PID control: Combines P, I, and D control for comprehensive control.
• Applications of Classical Control in Robotics:
• Manipulator control: Position, velocity, and force control of robotic manipulators
• Mobile robot control: Trajectory tracking and speed control of mobile robots
 A C T U A T O R S A N D S E N S O R S I N R O B O T I C C O N T R O L

Actuators are devices responsible for converting control signals into physical motion or action. They enable robots to move and interact
with their surroundings.
Types of Actuators:
• Electric Motors: Commonly used for precise control of joint movements in robotic arms.

• Pneumatic Actuators: Utilized for applications requiring high force but lower precision.

• Hydraulic Actuators: Ideal for heavy-duty applications with high force requirements.

Role in Robotic Control

• Actuators execute the desired actions or movements determined by the control system.

• They receive control signals, often in the form of voltages or currents, and convert these signals into mechanical motion.

Precision and Accuracy

• The choice of actuators influences the precision and accuracy of robotic movements.

• High-precision applications, such as surgical robots, may require precise electric actuators, while heavy-duty tasks might benefit from hydraulic
actuators.

Feedback Control
• Actuators are often equipped with feedback systems (e.g., encoders) to provide information about the actual position or velocity.

• This feedback is used in closed-loop control systems to ensure that the robot achieves and maintains the desired positions.
 A C T U A T O R S A N D S E N S O R S IN R O B O T IC C O N T R O L

Sensors provide robots with information about their environment, allowing them to perceive and respond to changes. Sensors play a crucial role
in enhancing the adaptability and autonomy of robotic systems.
Types of Sensors:
• Vision Sensors: Cameras and depth sensors for visual perception.

• Inertial Sensors: Accelerometers and gyroscopes for measuring acceleration and orientation.

• Force/Torque Sensors: Measure forces and torques applied to the robot's end-effector.

• Proximity Sensors: Detect the presence or distance of objects in the robot's vicinity.

Feedback for Control:

• Sensors provide real-time feedback about the robot's state, including its position, orientation, and environmental conditions.

• This feedback is essential for closed-loop control systems, enabling robots to adjust their actions based on the actual state of the system.

Collision Avoidance and Safety:

• Vision and proximity sensors help robots detect obstacles and avoid collisions.

• Safety sensors can immediately stop or alter robot movements in response to unexpected changes in the environment.

Autonomous Operation:
• Sensors contribute to the development of autonomous robots by providing data for navigation and decision-making.

• For example, robots equipped with lidar, and vision sensors can navigate through environments, avoiding obstacles and adapting to changing conditions.

Object Recognition and Manipulation:

• Vision sensors enable robots to recognize objects and determine their positions, supporting tasks like pick-and-place operations.

• Force/torque sensors assist in delicate tasks by providing feedback on the forces applied during object manipulation.
 I N T E G R A T I N G C O N T R O L W I T H A G E N T - B A S E D S Y S T E M S

Agent-based systems (ABS) are a decentralized approach to control, where multiple agents interact to achieve a common goal.
Integrating control with ABS can provide flexibility, adaptability, and robustness in complex robotic systems.

Challenges in Integrating Control and ABS:

• Information sharing and coordination among agents

• Conflict resolution and decision-making in decentralized systems

• Ensuring stability and convergence of the overall system

Potential Applications:

• Multi-robot collaboration: Coordinating multiple robots to perform tasks cooperatively

• Autonomous navigation: Adapting to changing environments and obstacles

• Human-robot interaction: Collaborating safely and effectively with humans

T H A N K Y O U