🦾Mechatronic Systems Integration Unit 7 – Industrial Robotics: Kinematics & Planning

Key Concepts and Terminology

• Industrial robotics involves the design, programming, and application of robotic systems in manufacturing and production environments
• Kinematics refers to the study of motion without considering forces, focusing on the position, velocity, and acceleration of robot joints and end-effectors
• Degrees of Freedom (DOF) represent the number of independent parameters that define the configuration of a robotic system
• Joints are the movable components of a robot that connect rigid links and enable relative motion between them (revolute, prismatic)
• End-effector is the device at the end of a robotic arm designed to interact with the environment (gripper, welding torch, paint sprayer)
• Workspace describes the total volume of space a robot can reach with its end-effector
• Singularity occurs when a robot's Jacobian matrix becomes non-invertible, leading to a loss of controllability in certain configurations

Robot Anatomy and Components

• Robotic systems consist of a series of rigid links connected by joints, forming a kinematic chain
• Actuators are the components responsible for generating motion in the robot's joints (electric motors, hydraulic cylinders, pneumatic actuators)
• Sensors provide feedback to the robot's control system about its internal state and external environment (encoders, force/torque sensors, vision systems)
• The robot's base is the fixed part that supports the manipulator and provides a reference frame for its motion
  • Stationary bases are fixed to the ground or a specific location
  • Mobile bases allow the robot to move within its environment (wheeled, legged, or aerial platforms)
• The robot's wrist is the set of joints near the end-effector that enables fine positioning and orientation control
• The controller is the computational unit that processes sensor data, executes control algorithms, and sends commands to the actuators

Forward Kinematics

• Forward kinematics determines the position and orientation of the end-effector given the joint angles or displacements of the robot
• The Denavit-Hartenberg (DH) convention is a systematic method for assigning coordinate frames to the links of a robotic manipulator
  • DH parameters (a, α, d, θ) describe the relative position and orientation between adjacent coordinate frames
• Homogeneous transformation matrices (HTMs) represent the spatial relationship between two coordinate frames
  • HTMs combine rotation and translation information into a single 4x4 matrix
• The forward kinematics equation calculates the end-effector's pose by multiplying the HTMs of each link in the kinematic chain: $T_n = T_1 \times T_2 \times ... \times T_n$
• The resulting HTM ($T_n$) describes the position and orientation of the end-effector with respect to the robot's base frame

Inverse Kinematics

• Inverse kinematics determines the joint angles or displacements required to achieve a desired end-effector position and orientation
• Inverse kinematics is more complex than forward kinematics due to the possibility of multiple solutions (robot configurations) for a given end-effector pose
• Analytical methods solve the inverse kinematics problem using geometric and algebraic techniques
  • Closed-form solutions exist for specific robot architectures (e.g., 6R manipulators with a spherical wrist)
  • Analytical methods are computationally efficient but may not be applicable to all robot designs
• Numerical methods iteratively search for a solution to the inverse kinematics problem
  • Jacobian-based methods (e.g., Newton-Raphson, Levenberg-Marquardt) use the robot's Jacobian matrix to update the joint angles incrementally
  • Optimization-based methods formulate the inverse kinematics problem as a minimization of an error function between the desired and current end-effector pose
• Redundant manipulators have more DOF than necessary to achieve a given task, leading to an infinite number of solutions for the inverse kinematics problem

Robot Motion Planning

• Motion planning generates a collision-free path for the robot to follow from an initial configuration to a goal configuration
• Configuration space (C-space) represents all possible configurations of the robot, considering both the robot's geometry and the obstacles in its environment
  • Free space (Cfree) is the subset of the C-space where the robot does not collide with obstacles
  • Obstacle space (Cobs) is the complement of the free space, representing the configurations where the robot collides with obstacles
• Sampling-based motion planning algorithms explore the C-space by randomly sampling configurations and connecting them to form a graph or tree
  • Rapidly-exploring Random Trees (RRT) incrementally build a tree of configurations by sampling random points in the C-space and extending the tree towards them
  • Probabilistic Roadmaps (PRM) construct a graph of collision-free configurations and connect them using local planning methods
• Graph search algorithms (e.g., A*, Dijkstra's) can be used to find the optimal path in the graph or tree generated by sampling-based methods
• Potential field methods define attractive and repulsive forces in the robot's environment to guide it towards the goal while avoiding obstacles

Trajectory Generation

• Trajectory generation creates a time-parameterized path for the robot to follow, specifying the position, velocity, and acceleration profiles for each joint
• Joint space trajectories describe the motion of individual joints over time, ensuring smooth and feasible movements
  • Polynomial interpolation methods (e.g., cubic, quintic) generate smooth joint trajectories by fitting polynomial curves to a set of waypoints
  • Trapezoidal velocity profiles consist of three phases: constant acceleration, constant velocity, and constant deceleration
• Cartesian space trajectories describe the motion of the end-effector in the task space, which is then mapped to joint space using inverse kinematics
  • Linear interpolation generates straight-line paths between waypoints in the Cartesian space
  • Circular interpolation creates arc-like paths by specifying intermediate points on a circle
• Trajectory optimization techniques (e.g., minimum jerk, minimum energy) generate trajectories that minimize specific cost functions while satisfying constraints
• Time scaling adjusts the velocity and acceleration profiles of a trajectory to ensure that the robot's physical limits (e.g., maximum joint velocities and accelerations) are not exceeded

Programming and Control Systems

• Robot programming involves specifying the desired behavior and actions of a robotic system using a suitable programming language or interface
• Teach pendant programming allows users to manually guide the robot to desired positions and record them as a sequence of points
  • The recorded points are then played back to execute the programmed motion
  • Teach pendant programming is intuitive but time-consuming and less flexible for complex tasks
• Offline programming uses simulation software to create and validate robot programs without the need for physical access to the robot
  • Offline programming allows for more complex tasks and optimizations but requires accurate models of the robot and its environment
• Robot Operating System (ROS) is an open-source framework that provides a set of libraries and tools for developing robot applications
  • ROS enables modular and distributed development, allowing components to communicate through a publish-subscribe messaging system
• Motion control algorithms ensure that the robot follows the desired trajectory accurately and robustly
  • Feedforward control calculates the required joint torques or forces based on the desired trajectory and the robot's dynamic model
  • Feedback control uses sensor measurements to correct for deviations from the desired trajectory in real-time (e.g., PID, computed torque control)
• Force control enables the robot to interact with its environment by regulating the contact forces and torques
  • Impedance control adjusts the robot's behavior to achieve a desired dynamic relationship between the applied force and the resulting motion
  • Admittance control maps the measured contact forces to desired motions, allowing the robot to react compliantly to external disturbances

Industrial Applications and Case Studies

• Material handling and pick-and-place operations are common applications of industrial robots, involving the movement of objects from one location to another
  • Bin picking requires the robot to identify, localize, and grasp objects from a container using vision and force sensing
  • Palletizing involves stacking and arranging objects on a pallet for storage or transportation
• Assembly tasks require precise positioning and insertion of components, often in collaboration with human workers
  • Robotic assembly cells combine multiple robots, sensors, and fixturing to automate the assembly process
  • Collaborative robots (cobots) are designed to work safely alongside humans, enabling flexible and efficient assembly operations
• Welding and fabrication processes use robots to improve consistency, quality, and productivity
  • Arc welding robots use electric arcs to join metal parts, following precise trajectories to ensure uniform welds
  • Spot welding robots use electrodes to create localized welds, commonly used in automotive manufacturing
• Painting and coating applications leverage the speed and repeatability of robots to achieve uniform and high-quality finishes
  • Spray painting robots use atomizers to apply paint or coatings evenly across surfaces
  • Electrostatic painting robots charge the paint particles and the target surface to ensure efficient and consistent coverage
• Inspection and quality control tasks employ robots equipped with various sensors to detect defects and ensure product conformity
  • Machine vision systems enable robots to capture and analyze images for dimensional verification, surface inspection, and object recognition
  • Non-destructive testing (NDT) robots use techniques like ultrasonic testing or X-ray imaging to detect internal flaws without damaging the product