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TRAJECTORY PLANNING

TRAJECTORY PLANNING. T. Bajd and M. Mihelj. Trajectory planning. The aim of trajectory planning is to generate the reference inputs to the robot control system, which will ensure that the robot end-effector will follow the desired trajectory. Trajectory between two points.

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TRAJECTORY PLANNING

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  1. TRAJECTORY PLANNING T. Bajd and M. Mihelj

  2. Trajectory planning The aim of trajectory planning is to generate the reference inputs to the robot control system, which will ensure that the robot end-effector will follow the desired trajectory.

  3. Trajectory between two points With industrial manipulators moving between two points we most often select the so called trapezoidal velocity profile.

  4. Trajectory between two points • Symmetric trajectory • Acceleration phase and and • Constant velocity phase

  5. Trajectory between two points • End of acceleration phase • After rearrangement • Duration of acceleration

  6. Trajectory interpolation between points • Acceleration phase • Constant velocity phase • Deceleration phase

  7. Interpolation by use of via points Trajectory consists of a sequence of linear segments describing the movements between two via points and parabolic segments representing the transitions through the via points.

  8. Interpolation by use of via points • Via points • Reached by the robot in time intervals • Interpolation functions • Polynomial coefficients to be determined

  9. Interpolation by use of via points • Velocities in linear segments • Computation of coefficients

  10. Interpolation by use of via points • Acceleration in a via point • Time of motion through the via point • Computation of coefficients • Velocity at equals and velocity at equals

  11. Interpolation by use of via points • Considering we obtain • Sum of the above equations leads to • Difference of the above equations leads to

  12. Interpolation by use of via points • Considering continuity of position at instant • and • leads to

  13. Interpolation by use of via points • In via point the trajectory deviates from the specified via point value by • The first and the last point on the trajectory are different from other via points and need to be addressed specifically. Namely, the initial and final robot velocity is usually zero and no deviations are allowed.

  14. Conditions in the initial point The lighter curve represents the trajectory without correction (position error can be noticed), while the darker curve shows the corrected trajectory

  15. Trajectory corrections • Small position changes are assumed in interval therefore • and • leading to

  16. Trajectory corrections • Duration of acceleration in the first point on the trajectory equals • or • where the initial acceleration equals

  17. Trajectory corrections • Similar correction is applied also for the last point • and • leading to • where

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