Backing-up Fuzzy Control of a Truck-trailer Equipped with a Kingpin Sliding Mechanism

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1 Backing-up Fuzzy Contro of a Truck-traier Equipped with a Kingpin Siding Mechanism G. Siamantas and S. Manesis Eectrica & Computer Engineering Dept., University of Patras, Patras, Greece gsiama@upatras.gr;stam.manesis@ece.upatras.gr Abstract For articuated vehices met in robotics and transportation fieds, even for an experienced operator, backing-up eads usuay to jack-knifing. This paper presents a fuzzy ogic controer for back-driving a truck-traier vehice into a predefined parking task. The truck-traier ink system is equipped with a kingpin siding mechanism acting as an anti-jackknife excitation input. By appying fuzzy ogic contro techniques, precise system mode is not required. The deveoped controer with thirty four rues works we as the presented simuation resuts demonstrate the avoidance of jack-knife and the accuracy of the backing-up technique. Introduction Contro of the backward movement of a truck and traier vehice, caed docking task, is known to be a typica noninear contro probem. The difficuty of the contro system design not ony causes the dynamics to be noninear, but aso emphasizes the inherent physica imitations of the system such as the jackknife phenomenon, a mathematica mode of which is discussed in (Fossum and Lewis 98). The contro system under investigation is not ony noninear but aso nonhoonomic. Backward movement contro of computer simuated truck-traiers using various types of inteigent contro e.g. fuzzy contro, neura contro and neurofuzzy or genetic agorithm-based contro (Yang et a. 26, Kiyuma et a. 24, Riid and Rustern 2), has been reported. The backing-up contro of a trucktraier is considered in (Park et a. 27) as a system with time deay. A fuzzy knowedge-based contro for backing muti-traier systems is aso considered in (Riid et a. 27). The kingpin siding mechanism, used in current work for backward stabiization, has been aso used for off-tracking eimination in mutiarticuated vehices (Manesis et a. 23). In this paper the kingpin siding mechanism is used mainy as an active anti-jackknife steering mechanism for backward motion. The mathematica mode of the considered system is different and more

2 374 Georgios Siamantas and Stamatis Manesis compex from that of a truck-traier without a kingpin siding mechanism. The precise mathematica description offers ony an initia guidance for writing the fuzzy rues of the controer. 2 System description - Fuzzy Logic Controer Design The system under consideration is a truck-traier vehice with on-axe siding-abe connection. Its geometry aong with the directions of a defined anges and axes are shown in Fig.. The major difference with a typica truck-traier system is the use of a siding kingpin on the rear axe of the tractor. The nomencature of the considered mode is: x, ) coordinates of the ( y truck s rear axe midpoint, x, ) coordinates of the traier s rear axe midpoint, ( y θ ange of the ongitudina axis of the truck w.r.t. the horizonta axis, θ ange of the ongitudina axis of the traier w.r.t. the horizonta axis, S ength of the kingpin side, truck s wheebase ength, ength between the traier s rear axe midpoint and the hinge joint, ϕ truck s steering whees turning ange, U truck veocity, S &,U 2 rate of change of the kingpin siding, α ange between the horizonta axis and the straight ine that passes from the axes origin and the x, ) point, d distance of the x, ) point from the horizonta axis (same as ( y y ), θ ( y α ange between the traier s ongitudina axis and the ine that passes from the axes origin and the ( x, y ) point, θ θ ange between the ongitudina axes of the truck and the traier. The kinematic equations of the system are the foowing: & x U cos y& = & U θ = 2 & θ = U S& = U x = x y = y θ = U sinθ tanϕ U + S tanϕ sin cosθ + S sinθ sinθ S cosθ ( θ θ ) sin S () The sin ( S / ) term was added to take into account the change of ange θ in case where the veocity U is zero and the rate of change of the kingpin siding

3 Backing-up Fuzzy Contro of a Truck-traier 375 U 2 is not zero. The above system mode wi be used in the evauation of the designed fuzzy ogic controer performance through simuations. Fig.. System geometry The main objective of this Fuzzy Logic Controer (FLC) is the backward motion contro of the truck and traier system to foow a target ine, a procedure simiar to parking. In the design of the fuzzy ogic controer we used 4 inputs ( α θ, θ θ, d, S ) and 2 outputs (ϕ, S & ). From the four inputs the first three are needed for achieving the contro objective and the fourth one ( S ) is needed to make S zero when the first two inputs become zero. The input and output variabes were defined to have 5 membership functions each: NL: Negative Large, NS: Negative Sma, ZE: Zero, PS: Positive Sma, PL: Positive Large. The normaized degree of membership function diagrams for each input or output variabe are shown in Fig. 2. For the input variabes the NS, ZE, PS membership functions are trianguar and the NL, PL are trapezoida. The output variabes have a 5 membership functions trianguar. The fuzzy ogic controer has been deveoped by defining 34 ogica rues shown in Fig. 3. These rues are consistent with the foowing evauation strategies: () the truck s steering whees must turn in such a way as to make the system move towards the direction that makes the ange α θ zero, (2) if the anges α θ and θ θ beong to the ZE degree, i.e. the truck-traier system is moving towards the axes origin and the ange between the truck and the traier is cose to zero, then we can turn the truck s steering whees in such a way as to minimize the distance d from the horizonta axis, (3) if the ange θ θ is arge (NL, PL degrees) and to avoid jackknifing, regardess of the vaues of a other variabes, the steering whees shoud be turned in such a way as to minimize the ange θ θ, (4) the kingpin siding shoud have a direction opposite to the centrifuga direction and must be proportiona to the ange θ θ. This action wi provide greater cor-

4 376 Georgios Siamantas and Stamatis Manesis rection margin to the steering whees to avoid jackknifing, (5) if the anges α θ and θ θ beong to the ZE degree, i.e. the truck-traier system is moving towards the axes origin and the ange between the truck and the traier is cose to zero, then we can make the kingpin siding distance zero by appying opposite S & proportionay to S. The inguistic rues that were used have the genera form: IF [INP is MF INP ] AND [INP 2 is MF INP2 ] THEN [OUT is MF OUT ] The fuzzy operator AND and the impication method were defined as minimum. The centroid defuzzification method was used. The output aggregation method was defined as sum. We have chosen the sum method instead of the maximum method because it fits better to the cumuative contro method imposed from strategy no. 2 used in controing the distance d over the contro of the α θ ange. Fig. 2. Normaized degree of membership function diagrams of input-output variabes Fig. 3. Fuzzy Logic Controer ogica rues

5 Backing-up Fuzzy Contro of a Truck-traier Simuations, Motion Restrictions, Advantages of Kingpin Siding To verify the effectiveness of the proposed fuzzy controer we performed severa tests in a simuation environment. The simuation mode was based on equations () with the foowing assumptions: U is - m/sec, is 4 m, is 6 m, ϕ varies between -5 and 5, ϕ& varies between -3 /sec and 3 /sec, S varies between -.6 m and.6 m and S & varies between -. m/sec and. m/sec. Because the designed membership function diagrams are normaized we used gains in the inputs and outputs to change their universes of discourse scaes. Severa simuation tests were performed, from different system initia positions and directions, with and without kingpin siding contro. In Fig. 4, we see the system response from initia conditions x, y, θ, ) = (6, -, 45, -45). We see ( θ that kingpin siding contro does not have big infuence in system response as far as concerning the trajectory of the system. The difference is that we have greater ange margin for the contro of a possibe jackknife situation in the case where kingpin siding contro is used. This can be shown from simuations and aso from the system geometry where we see that with a kingpin siding aong the centripeta direction we gain approximatey sin ( S / ) = 5.74 in θ θ ange and by extension to the steering whee ange ϕ. The positive effects of this ange gain are demonstrated in Fig. 5 where the initia conditions are (6, 2, 45, -45). In these responses the turn imit of the truck s steering whees is between -35 and 35. It is obvious that without kingpin siding contro the system enters a jackknife condition, Fig. 5 (eft). The system with kingpin siding contro avoids jackknife, Fig. 5 (right). It shoud be noted that when the truck-traier system is moving backwards the advantages of kingpin siding contro appear during siding towards the centripeta direction in contrast with the system moving forward where the advantages appear during siding towards the centrifuga direction. Fig. 4. System response from initia conditions (6, -, 45, -45). Without siding contro (eft), with siding contro (right)

6 378 Georgios Siamantas and Stamatis Manesis Fig. 5. System response from initia conditions (6, 2, 45, -45) and (-35, 35 ) steering whee ange imit. Without siding contro (eft - jackknife), with siding contro (right) 4 Concusions A fuzzy ogic controer was designed for the backward motion of a truck-traier system with on-axe kingpin siding. Various tests were conducted to test the controer effectiveness. The controer showed good performance with the system starting from various initia conditions. The use of kingpin siding towards the centripeta direction has no adverse effect in system response whie it reduces the maximum turn of the truck s steering whees when the system is maneuvering backwards. This gives greater steering whee turn margin for the truck to avoid jackknife. References. Fossum TV., Lewis GN. A mathematica mode for traier-truck jackknife. SIAM Review (98); vo.23, no.: Kiyuma A., Kinjo H., Nakazono K., Yamamoto T. Backward contro of mutitraier systems using neurocontroers evoved by a genetic agorithm. Proceedings 8th Internationa Symposium on Artificia Life and Robotics (24); pp Manesis S., Koussouas N., Davrazos G., On the suppression of off-tracking in mutiarticuated vehices through a movabe junction technique. Journa of Inteigent and Robotic Systems (23); vo.37: pp Park C.W., Kim B.S., Lee J., Digita stabiization of fuzzy systems with time-deay and its appication to backing up contro of a truck-traier. Internationa Journa of Fuzzy Systems, (27), vo.9, pp Riid A., Ketoa J., Rustern E., Fuzzy knowedge-based contro for backing muti-traier systems. Proceedings IEEE Inteigent Vehices Symposium, (27), pp Riid A., Rustern E. Fuzzy ogic in contro: Track backer-upper probem revisited. Proceedings th IEEE Internationa Conference on Fuzzy Systems (2); vo.: pp Yang X., Yuan J., Yu F. Backing up a truck and traier using variabe universe based fuzzy controer. Proceedings IEEE Internationa Conference on Mechatronics and Automation (26); pp