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A linear model of the car along the longitudinal component of the path is represented in figure long_block.jpg. Symbols represent
- PWM: the motor input signal.
- const_: a constant term representing friction.
- W(s)_: transfer function between PWM signal and speed.
- v: 2D speed of the car.
- y^.y': monodimensional speed obtained by projecting the 2D speed of the car on the path.
- y: monodimensional position of the car obtained by projecting its 2D position on the path.
- y_mym: monodimensional position of the car measured by cameras.
- D_aDa: actuator disturbances on the control variable.
- D_slope: disturbances on Dslope: the test-bed is not perfectly flat but it is slightly inclined. This has been found to considerably affect the speed caused by slopes of the test-bed.
- D_slipDslip: disturbances on the speed caused by the coupling with the lateral dynamics of the car (i.e. with the steer).
- D_proj: disturbances caused by Dproj: projecting the 2D speed on the path is modeled here as a disturbance.
- D_jump: Djump: the path followed by cars is composed by a polygonal chain. This means that when the car goes from a segment to the next one, there is an interval of time during which the car position is projected on the same exact point of the path. This disturbance compensate for the fact that the actual 1D speed of that car in that point is 0.
- D_m: measurement error.
D_slope and D_slip are path dependent. I plan to measure them experimentally and treat them as a path-dependent known disturbance.
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D_jump ANALYSIS
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- . For example, in Figure Djump.png the car goes through the trajectory A-B-C-D. While in the arc B-C, the vehicle position is projected on the path always in the same point P. Similar considerations can be done when a car cuts a corner. This disturbance is modeled with a negative (or positive in case the vehicle cut the corner) step that corrects the position each time the vehicle changes the segment of a path. Essentially, this is a measure of the difference between the length of the nominal path and the lenght of the actualy trajectory that the car follows.
- Dm: measurement error of the cameras.
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Djump
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The path fig8 is composed by 649 control points for a total length of 9465.53 millimeters. The angle difference between two consecutive segments is delta = 0.9 degrees. We set the maximum distance of the car from the path to be x_max xmax = 30cm (which is realistic with the current steer control performances). Assuming the car to constantly be at the maximum distance for the whole time x coordinate (distance from the path) to be constant at xmax, we can compute D_jump Djump = 649 * delta * x_max xmax = 3058.34mm which is the 32.31% of the path length. It is clear thus that the steer control performance must be drastically improved to reduce this effectaffects considerably the behavior of the car. Consequently lots of efforts should be done to improve it.
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Dslope and Dslip
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Dslope and Dslip are path dependent. I plan to measure them experimentally and treat them as a path-dependent known disturbance.
CPS
CAMERA MEASUREMENT ERROR CORRECTION
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