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Mobile Robot Predictive Trajectory Tracking

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Trajectory tracking: accurately follow a given time-indexed path in the plane ... Adaptation of the algorithm for 4-wheeled autonomous vehicles ... – PowerPoint PPT presentation

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Title: Mobile Robot Predictive Trajectory Tracking


1
Mobile Robot Predictive Trajectory Tracking
Martin Seyr, Stefan Jakubek
2
Overview
  • Problem statement
  • Introduction of the mobile robot
  • Outline of the general idea of the proposed
    algorithm
  • Presentation of the key innovations
  • Technical details
  • Results
  • Conclusion and outlook

3
Problem statement
  • Trajectory tracking accurately follow a given
    time-indexed path in the plane
  • Nonlinear nonholonomic system
  • Cannot be stabilized by continuous,
    time-invariant feedback
  • Cannot be feedback-linearized
  • Account for non-zero side-slip
  • Posture stabilization and tracking using the same
    algorithm
  • Most approaches deal with only one of the two
    tasks

4
The mobile robot
  • Cuboid with 0.075m square footprint
  • 2 DC-motors driven by PWM-input voltage
  • DSP executes algorithm
  • mC provides sensor data and generates PWM-signal
  • Dual full bridge driver amplifies control voltage
  • Autonomous differential drive mini robot
    Tinyphoon, equipped with an Infineon XC167
    microcontroller and an AD BF533 digital signal
    processor

5
Control concept
  • Cascaded control scheme
  • Inner loop velocities are controlled via state
    feedback control with integration of the control
    error
  • Outer loop nonlinear predictive control using
    the closed inner loop dynamics equation for
    prediction
  • Reference velocities as input into the closed
    inner loop are calculated using
    Gauss-Newton-optimization

6
Key innovations
Predictive control in combination with cascade,
state space formulation of closed loop dynamics
used for prediction
Compensation of the algorithms calculation time
using an extended state space system and
predicted velocities in the control law
The inevitable side-slip during sharp turns is
accounted for by modifying the reference angle
accordingly power slide possible
7
Velocity dynamics
  • Linearization by
  • Neglecting slip dynamics
  • Effective track speed
  • Least-squares-linearization of the motor
    characteristic
  • State space formulation

Kinematics of the unicycle-type mobile robot
including side-slip
8
Kinematics
  • Unicycle-type kinematics including side-slip
  • Relationship between attitude and path angle

9
Control of the inner loop
  • Discretization of the linear state space system
  • Extended linear discrete system with integration
    of the control error
  • Stabilizing effect of exact past velocities
    exploited
  • State feedback control law obtained by pole
    placement or LQR-technique

10
Control of the outer loop I
  • Discretization of the nonlinear state space
    representation of the kinematics
  • Minimization of a scalar quadratic cost function
    during every sampling interval
  • To stabilize the solution and reduce the
    calculation time, shape functions are chosen

11
Control of the outer loop II
  • Estimation of the side-slip angle by
    Spline-interpolation
  • Corrected attitude angle calculated by
  • Side slip assumed to be constant in future

12
Control of the outer loop III
  • Minimization of the cost function by
    Taylor-series expansion
  • Total derivatives of positions with respect to
    form parameters calculated recursively

13
Control of the outer loop IV
  • Additional terminal constraint on attitude angle
    using a linearized Lagrangian side condition
    further stabilizes the solution
  • Final form of the system of equations of
    dimension 5 to be solved
  • With the resulting form parameters the reference
    velocities are updated and the control law of the
    inner loop is used to calculate the PWM-inputs

14
Tuning parameters
  • Sampling time
  • Poles of the inner loop
  • Prediction horizon
  • Weight matrices L and R
  • Shape functions
  • Number of iterations performed

15
Simulation results I
  • Simulation Video normal/8x slow motion
  • Sharp turn at 1ms-1 track speed, side-slip angle
    over 25, minimum radius 0.27m
  • Side-slip angle control power slide

16
Simulation results II
17
Experimental results
  • Experiment Video normal speed
  • Square with 0.5m side length, circle with 0.25m
    diameter, peak velocity 0.88ms-1, peak yaw rate
    12.3rads-1
  • So far only wheel-encoders implemented, therefore
    no side-slip angle control possible

18
Outlook and Further Work
  • Implementing and testing of the adaptive extended
    Kalman filter for inertial navigation
  • Adaptation of the algorithm for 4-wheeled
    autonomous vehicles
  • Trajectory planning under consideration of static
    and dynamic obstacles

19
Final Remarks
  • Thank you for your attention!
  • Further Questions?
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