🤖Robotics Unit 3 – Robot Dynamics and Control

Key Concepts and Terminology

• Robot dynamics involves the study of forces and torques that cause motion in robotic systems
• Kinematics focuses on the geometric relationships between joint positions, velocities, and accelerations without considering forces
• Degrees of freedom (DOF) refer to the number of independent parameters that define a robot's configuration
• Forward kinematics determines the end-effector position and orientation given joint angles or positions
• Inverse kinematics calculates joint angles or positions required to achieve a desired end-effector pose
• Jacobian matrix relates joint velocities to end-effector velocities and is crucial for robot control
• Singularities occur when a robot loses one or more DOF, leading to control difficulties

Robot Kinematics

• Forward kinematics uses homogeneous transformation matrices to describe the spatial relationships between robot links
  • Denavit-Hartenberg (DH) parameters are commonly used to define these transformations
  • DH parameters include link length, link twist, joint offset, and joint angle
• Inverse kinematics can be solved analytically for simple robot geometries (2-link planar robot) or numerically for complex structures
  • Numerical methods include Jacobian-based approaches (Jacobian transpose, pseudoinverse) and optimization techniques
• Velocity kinematics relates joint velocities to end-effector velocities using the Jacobian matrix
  • The Jacobian matrix is obtained by differentiating the forward kinematics equations
• Manipulability measures the robot's ability to move in different directions and avoid singularities
  • Manipulability ellipsoids visualize the robot's velocity and force capabilities

Robot Dynamics

• Dynamics considers the forces and torques that cause motion in robotic systems
• The equations of motion describe the relationship between joint torques, joint positions, velocities, and accelerations
  • These equations are derived using Lagrangian mechanics or Newton-Euler formulation
• Lagrangian dynamics uses the difference between kinetic and potential energy to formulate the equations of motion
  • Generalized coordinates (joint angles) and generalized forces (joint torques) are used in this approach
• Newton-Euler dynamics recursively computes the forces and torques acting on each link, considering the motion of the previous link
  • This method is computationally efficient for real-time control
• Inertial parameters (mass, center of mass, inertia tensor) are essential for accurate dynamic modeling
  • These parameters can be estimated through system identification techniques

Control Systems for Robots

• Robot control aims to make the robot follow desired trajectories or apply desired forces
• Joint space control involves controlling individual joint angles or positions
  • PID (Proportional-Integral-Derivative) control is commonly used for joint space control
  • Computed torque control uses the dynamic model to linearize the system and apply feedback control
• Operational space control focuses on controlling the end-effector position and orientation
  • Inverse dynamics control computes the required joint torques based on desired end-effector accelerations
• Impedance control regulates the relationship between the robot's motion and the forces it applies to the environment
  • This control scheme is useful for interaction tasks and compliant motion
• Adaptive control techniques (model reference adaptive control) can handle uncertainties and variations in robot parameters

Sensors and Actuators

• Sensors provide information about the robot's internal state and its environment
  • Encoders measure joint positions and velocities
  • Inertial Measurement Units (IMUs) provide orientation and acceleration data
  • Force/torque sensors measure the interaction forces between the robot and the environment
• Actuators generate motion in robotic systems
  • Electric motors (DC, brushless, stepper) are widely used due to their precision and controllability
  • Hydraulic actuators offer high power density and are suitable for heavy-duty applications
  • Pneumatic actuators are lightweight and compliant, making them safe for human-robot interaction
• Sensor fusion techniques (Kalman filtering) combine data from multiple sensors to improve state estimation

Motion Planning and Trajectory Generation

• Motion planning involves finding a feasible path from a start configuration to a goal configuration
  • Sampling-based methods (Rapidly-exploring Random Trees, Probabilistic Roadmaps) efficiently explore high-dimensional configuration spaces
  • Optimization-based methods (CHOMP, TrajOpt) generate smooth and optimal trajectories
• Trajectory generation creates time-parameterized paths that satisfy kinematic and dynamic constraints
  • Polynomial interpolation (cubic, quintic) is commonly used for smooth trajectory generation
  • Trapezoidal velocity profiles provide simple and efficient trajectories for point-to-point motions
• Obstacle avoidance is a crucial aspect of motion planning
  • Potential field methods create a virtual force field to guide the robot away from obstacles
  • Geometric methods (A*, Dijkstra) find shortest paths in discretized environments

Robot Programming and Simulation

• Robot programming languages (ROS, RAPID) provide high-level interfaces for controlling and simulating robots
  • These languages often include libraries for kinematics, dynamics, and motion planning
• Simulation environments (Gazebo, V-REP) allow testing and debugging of robot control algorithms
  • Physics engines (ODE, Bullet) simulate realistic dynamics and interactions
• Machine learning techniques (reinforcement learning) enable robots to learn and adapt to new tasks
  • Deep learning (convolutional neural networks) is used for perception and decision-making in robotic systems

Applications and Case Studies

• Industrial robotics involves the use of robots in manufacturing and assembly tasks
  • Examples include welding, painting, pick-and-place, and material handling
• Service robotics focuses on robots that assist humans in various environments
  • Domestic robots (vacuum cleaners, lawn mowers) perform household tasks
  • Healthcare robots (surgical robots, rehabilitation robots) aid in medical procedures and patient care
• Mobile robotics deals with robots that can navigate and operate in different environments
  • Autonomous vehicles (self-driving cars) rely on robot perception and control techniques
  • Unmanned Aerial Vehicles (UAVs) are used for aerial mapping, inspection, and delivery
• Space robotics involves the development of robots for space exploration and satellite servicing
  • Mars rovers (Curiosity, Perseverance) are examples of successful space robotics missions