Title: Mobile Robot Predictive Trajectory Tracking
1Mobile Robot Predictive Trajectory Tracking
Martin Seyr, Stefan Jakubek
2Overview
- 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
3Problem 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
4The 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
5Control 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
6Key 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
7Velocity 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
8Kinematics
- Unicycle-type kinematics including side-slip
- Relationship between attitude and path angle
9Control 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
10Control 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
11Control 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
12Control 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
13Control 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
14Tuning parameters
- Sampling time
- Poles of the inner loop
- Prediction horizon
- Weight matrices L and R
- Shape functions
- Number of iterations performed
15Simulation 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
16Simulation results II
17Experimental 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
18Outlook 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
19Final Remarks
- Thank you for your attention!
- Further Questions?