Please enable JavaScript.

Coggle requires JavaScript to display documents.

IA368N (Motion control (kinematics (:check: generalized coordinates (q),…

- - - - move all the points in the same direction
      - vector
      - Homogeneous matrix
        
        IrOP = IrOB + IrBP (only if expressed in the same coord. system)
        
        IrOP = IrOB +RIB * BrBP (if expressed in different coord. system
    - - math
        
        I_r = R_IB B_r
        (=) B_r = R_BI I_r
        (=) R_BI = R_IB (Transposto)
      - restrictions
        
        one point is always fixed and other points rotate around it
        
        consecutive rotations are multiplication of corresponding matrices (R_CI= R_CB R_BI)
    - - we can’t add vect. expressed in different frames
      - angular velocity is the same at any point of the body
    - - set of independent variables
      - uniquely describe robot's configuration
      - Denavit-Hartenberg parameters for industrial manipulators
      - for us any q will be composed by a unique relative angle at the join
    - - map changes (deltas / velocities) from q to Cartesian space
        
        Cartesian velocities to q velocities: Express contact constraints and Trajectory control
        
        q to Cartesian space: Forward and Inverse kinematics
        
        :warning:Problem approach (Interactively)
        
        Start from known solution (e.g. given by forward kinematic)
        
        Linearize the function rOF(q) around the solution
        resulting in the Jacobian that maps deltas in
        generalized coord. to deltas in Cartesian space
        
        Invert the Jacobian to obtain detla q
        
        Update generalized coordinates
      - Differential kinematics
        
        Robot control also requires general velocities as general coordinates
- - - - both
        
        design bot for tasks
        
        design control
    - - I is inertial and arbitrary
- - - - Encoder/odometry
        
        Microcontrolador
        
        Calc couting interruptions
      - Heading
        
        Gyroscope
        
        Angula velocity
        
        Accelerometer
        
        IMU
        
        Magnetometer
    - - GPS
        
        Differential GPS
        
        8 meters precision
        
        Indoor
        
        StarGazer
      - Camera
        
        Mono