Introduction to Robotics

• Robotics integrates computer science, engineering, and other disciplines to design, construct, operate, and apply robots
• Robots are programmable machines with electromechanical parts
• Control is achieved via computer programs or electronic circuitry
• Robots can perform tasks autonomously or semi-autonomously

Robot Components

• Actuators drive robot movement, examples: electric motors, pneumatic, and hydraulic cylinders
• Sensors provide environmental or internal state information: cameras, force, and tactile sensors
• Controllers process sensor data and command actuators using algorithms and software
• Power supplies, such as batteries, provide energy to the components

Types of Robots

• Industrial robots are for manufacturing, assembly, and material handling
• Service robots assist humans in cleaning, delivery, and healthcare
• Mobile robots navigate warehouses, hospitals, and outdoor terrains
• Humanoid robots mimic human movements and behaviors

Degrees of Freedom (DOF)

• DOF defines the configuration of a mechanical system through independent parameters
• For robots, DOF corresponds to the number of independently moving joints
• Each DOF represents a direction or axis of movement or rotation
• More DOF provides greater flexibility and dexterity

Joints and Links

• A joint connects rigid bodies (links), allowing relative motion
• Revolute joints (rotational joints) allow rotation around an axis
• Prismatic joints (linear joints) allow translation along an axis
• A link is a rigid body connecting two or more joints

Kinematics

• Kinematics studies motion without considering forces that cause motion
• In robotics, kinematics relates joint positions to end-effector position and orientation
• Forward kinematics determines the end-effector pose from joint variables
• Inverse kinematics determines joint variables needed for a desired end-effector pose

Forward Kinematics

• Calculates end-effector position and orientation based on known joint angles or positions
• This is a direct problem with a unique solution for non-redundant robots
• The Denavit-Hartenberg (DH) convention models robot kinematics

Denavit-Hartenberg (DH) Convention

• DH parameters are a set of four parameters associated with each link of a robot manipulator:
  • Link length (a): the distance between the two joint axes
  • Link twist (α): the angle between the two joint axes
  • Joint offset (d): the distance between the two common normals
  • Joint angle (θ): the angle between the two common normals
• DH parameters create homogeneous transformation matrices describing relationships between adjacent link coordinate frames
• Multiplying these transformation matrices yields the transformation from the base frame to the end-effector frame

Homogeneous Transformation Matrices

• A homogeneous transformation matrix is a 4x4 matrix that represents rotation and translation in 3D space
• Transforms points and vectors from one coordinate frame to another
• The upper-left 3x3 submatrix represents rotation
• The rightmost 3x1 column vector represents translation
• Homogeneous transformation matrices represent complex transformations as a single matrix multiplication

Inverse Kinematics

• Determines joint angles or positions to achieve a desired end-effector pose
• This is an inverse problem with multiple, no, or infinite solutions
• Solutions are obtained via analytical or numerical methods

Analytical Solutions

• Derives closed-form equations directly relating end-effector pose to joint variables
• Analytical solutions are typically faster and more accurate than numerical ones
• They can be difficult or impossible to obtain for complex robot geometries

Numerical Solutions

• Uses iterative algorithms to minimize the error between desired and actual end-effector poses
• Can be applied to a wider range of robot geometries
• Can be slower and less accurate than analytical solutions and may not always converge

Singularity

• Occurs when the robot loses one or more degrees of freedom, making certain end-effector poses unreachable
• The robot's Jacobian matrix becomes singular, and the inverse kinematics solution becomes undefined or unstable
• Singularities can cause large joint velocities or forces
• Limit the robot's ability to perform certain tasks
• Singularities are avoided by careful robot design, trajectory planning, and workspace analysis