Page 37 - Toucpad robotics C11

Forward Kinematics: Calculate the position and orientation of the robot’s end-effector (e.g., its gripper) given
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the angles of its joints. Imagine a robotic arm with multiple segments and joints; if you know the angle of each
joint, you can determine exactly where the hand is in space.
Inverse Kinematics: This is the reverse and often more challenging problem: given a desired position and
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orientation for the robot’s end-effector (where the robot’s hand needs to be), calculate the required angles for
each of its joints. This is essential for guiding a robot to pick up an object at a specific location.
Example: For a robotic arm assembling a circuit board, inverse kinematics is used to calculate the precise joint
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angles required for the gripper to reach a tiny electronic component, pick it up, and place it accurately on the
board.
Dynamics: This branch of physics deals with the forces that cause motion. In robotics, dynamics is used to:
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Understand how forces and torques affect a robot’s movement.
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Calculate the required motor power to move specific loads.
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Analyse stability (e.g., preventing a walking robot from falling).
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Example: When a robot arm lifts a heavy object, dynamics helps engineers calculate how much torque the
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motors at each joint need to apply to lift the object smoothly and without the arm collapsing under the weight.
This also helps in designing the structural strength of the robot’s links.

Forces and Torque (Newton’s Laws)
Newton’s Laws of Motion are foundational. Robots operate by applying and reacting to forces.
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Newton's First Law (Inertia): A robot in motion tends to stay in motion, and a robot at rest tends to stay at rest,
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unless acted upon by an external force. This is important for understanding how much force is needed to start or stop
a robot’s movement.
Newton's Second Law (F=ma): Force equals mass times acceleration. This law is fundamental for calculating the
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forces required to accelerate or decelerate parts of the robot, or to apply a specific force to an object.
Newton's Third Law (Action-Reaction): For every action, there is an equal and opposite reaction. This is critical for
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understanding ground reaction forces in walking robots, or how a robot’s push on an object will result in a reaction
force back on the robot.
Torque: This is the rotational equivalent of force. It’s the twisting force that causes rotation around an axis. Motors
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generate torque to move robot joints, wheels, or propellers.
Example: For a quadcopter drone, the thrust force generated by its propellers (related to Newton’s Third Law) is
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calculated using aerodynamic principles to counteract gravity and achieve lift. To rotate (yaw) or tilt (pitch/roll), the
drone’s control system adjusts the torque of individual motors, demonstrating how forces and torques dictate its
movement.
Control Systems (Feedback and Stability)
A robot’s ability to perform tasks precisely relies on sophisticated control systems, which are deeply rooted in physics
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and mathematics.
Feedback Control: Robots constantly measure their current state (e.g., position, speed) using sensors and compare
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it to their desired state. The difference (error) is used by the control system to generate commands to the actuators,
correcting the robot’s movement. This continuous loop is called feedback control.
Stability: A crucial aspect of robot control is ensuring stability. A control system must prevent oscillations or runaway
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movements. For instance, a walking robot must maintain balance, and a drone must maintain a stable flight path
even in windy conditions. Physics principles of equilibrium and oscillations are directly applied here.
Example: Consider a robotic arm trying to hold a heavy object steady. Gravity exerts a force on the object. The robot’s
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force sensors (physics) detect this force. The control system (mathematics/algorithms) constantly measures the
current position and compares it to the desired steady position. If the arm starts to sag, the control system calculates
the required torque (physics) for the motors to apply to correct the position, forming a continuous feedback loop to
maintain stability.
35
Introduction to Robots: What Exactly are They?