The haptic interface force feedback is one of the key factors for a reliable flight simulation. This paper addresses the design and control implementation of a simple joystick-like haptic interface to be used for a helicopter flight simulator. The expression of the haptic interface force is obtained by dynamic analysis of the haptic interface operation. This paper proposes a new strategy aiming at avoiding the use of an expansive and complex force/torque sensor. Accordingly, specific dynamic model is implemented by including Stribeck friction to describe the friction moment. Experimental data are processed as based on a genetic algorithm for identifying the dynamic parameters in the Stribeck friction model. This allows to obtain the friction moment parameters of the haptic interface, as well as the torque distribution due to gravity and the rotational inertia parameters of the haptic interface for the calculation of the haptic interface force. Experimental tests are carried out and results are used to validate the proposed dynamic model and dynamic parameter identification method and demonstrate the effectiveness of the proposed force feedback while using a cheap photoelectric sensor instead of an expansive force/torque sensor.
Due to the high risks and costs of training on a real helicopter, pilots often need to complete a preliminary training on a helicopter flight simulator. Real flight training is carried out only after a successful training on a simulator. In helicopter flight simulators, the joystick is a key element, which is used to achieving a reliable helicopter driving while providing a force feedback feeling, which needs to properly mimic the force feedback feelings of a real helicopter flying (Prachyabrued and Robert, 2018). In the real flight control process, the pilot's hand will feel the feedback force and make judgments, then adjust the flight status through the feedback force. In the whole process, the current force of the haptic interface needs to be used as the simulation calculation of the feedback force. Thus, its measurement accuracy is particularly important. Most of the operating forces are measured by using torque sensors. The papers Cavallo et al. (2004), Rinaldi and Beckham (1983), Hutton et al. (1994), and Fergani et al. (2016) installed a pull-up/pressure sensor at the end of the rod to read the applied force at each moment. However, torque sensor occupies large space in both mechanical installation and wiring, which affects the normal operation of the pilots. This paper proposes a different strategy aiming at avoiding the use of an expansive and complex force/torque sensor. Namely, the proposed approach is based on establishing a reliable dynamic model of the haptic interface to replace the role of the force/torque sensor. Accordingly, a proper dynamic model and a parameter identification strategy have been proposed.
In a servo system, there are complex rolling friction and sliding friction phenomena between gear train, bearing, input/output shaft and seal. Therefore, the modelling of friction torque is very important, which directly affects the dynamic accuracy of the haptic interface. A variety of empirical models have been proposed for friction calculation of servo system, which can be divided into two phases: static friction model and dynamic friction model (Bona and Indri, 2005). The most widely used static friction model is the Stribeck model. Several papers analyzed the friction of a servo system by establishing its Stribeck friction model (Lichun and Pavelescu, 1982; Xu et al., 2011; Chen et al., 2016; Márton and Lantos, 2009; Broel-Plater et al., 2018). Considering the advantages and drawbacks of the existing models in literature, it has been decided to implement a Lugre model to analyze the friction of the servo system, as proposed in Canudas de Wit et al. (1995), Wang et al. (2019), Azizi and Yazdizadeh (2019), Freidovich et al. (2010), and Ishikawa et al. (2010). Main advantage of Lugre model is its relatively high accuracy, while its implementation is relatively complex, since it introduces an unknown quantity which can be difficult to be measured directly and requires a high precision servo system. The Stribeck model is currently used in many fields to model the friction moment. Since there are unknown parameters in the haptic interface dynamics model, such as gravity moment, Stribeck friction moment model parameters and rotational inertia, these parameters need to be identified. The main available parameter identification methods are tracing methods, least square methods, and genetic algorithms. The genetic algorithms are very effective evolutionary random search methods, which are proven in literature to be very effective in managing non-linear problems with a high level of computational robustness and calculation parallelization. Accordingly, genetic algorithms can be seen as the most convenient approach for addressing this identification problem. In this paper, a dynamic analysis is carried out on the a 2-dof flight haptic interface for a helicopter simulator. A nonlinear Stribeck model is established for the friction torque of the servo system. A curve fitting and genetic algorithm method are used for processing the data to identify the gravity torque, four parameters of the Stribeck model and the rotational inertia. Finally, the available parameters identified are brought into the dynamic model to calculate the haptic interface force in real time and an experimental validation is carried out to proof the effectiveness of the proposed approach.
This paper adopts the helicopter simulator at laboratory in Yanshan University which is shown in Fig. 1. The helicopter flight simulator is mainly composed of four modules: a helicopter simulation cockpit system, a virtual scene system, a dynamic motion system and an audio system. The simulator's haptic interface is shown in Fig. 2. The haptic interface is driven by two servomotors, and two disc speed reducers are used for speed regulation. The motor adopts Kollmorge CKM04 AC permanent magnet synchronous servo motors, and its corresponding AKD series servo driver supports Modubus TCP communication. The parameters of the servo motors and the reducers are shown in Tables 1 and 2. The hardware system composition of the haptic interface is shown in Fig. 3.
The helicopter simulator in Yanshan University.
Force feedback test bench of haptic interface.
Hardware system composition of haptic interface.
First, the computer is connected to the switch, and the switch is connected
with two motor drivers respectively through Enternet port. Then, C
Parameter of the Kollmorge CKM04 servo motor.
Parameter of the reducers.
First, coordinate system for the haptic interface is established for the
haptic interface, as shown in Fig. 4. The intersection point of the two
motor axes is defined as origin
Haptic interface coordinate system.
The free-body diagram is shown in Fig. 5. The angle
When the haptic interface moves, the control handle, the haptic interface
and the base of the haptic interface move at an angle
The proposed free-body diagram.
In Fig. 5,
The Lagrange method is adopted to conduct dynamic analysis of the system.
The Lagrange function can be formulated as
The total kinetic energy
The potential energy of the haptic interface
Especially, the torque output
Since the armature inductance of
In the haptic interface structure, there are complex frictions within the servo motor and between the reducer. The friction torque generated by these frictions has a great influence on the accurate modelling of the haptic interface. Therefore, the friction torque at each moment must be accurately obtained to ensure the accuracy of the calculated force and torque at each moment.
The classic Coulomb friction model friction indicated that friction force is related to the positive pressure acting on the object. However, due to the lubrication in the servo system, the influence of viscous friction must be considered.
Stribeck proposed to model the servo friction as a combination of Coulomb
friction and viscous friction. He has given a quantitative formulation for
friction with respect to velocity (Balogh and Krstic, 2004). Similarly, the
Stribeck formula can be converted into the formula of friction torque
regarding motor speed as proposed in (Iwasaki et al., 1999):
The Stribeck curve is related to the speed of the servo system. In the low-speed area, it is affected by Coulomb friction and viscous friction, and the friction torque decreases. This area is called boundary lubrication friction area. With the increase of speed, the influence of viscous friction is much higher than Coulomb friction. At this time, the friction torque is approximately proportional to the rotational speed. This operation condition is defined as liquid lubrication condition.
There are two problems in applying the Stribeck friction model to the control of haptic interface force control: on the one hand, it is difficult to describe the change of haptic interface friction torque when the velocity is zero; on the other hand, the change of velocity near the zero point will cause a sudden change of friction torque, which will lead to a jitter in the reversing process. Therefore, approximate treatment of the low speed phase of the Stribeck friction model is required. This paper proposes to use a sigmoid function to deal with Stribeck friction model (Ciliza and Tomizuka, 2007).
The Stribeck friction torque model improved by sigmoid function can be
expressed as follows:
According to Eq. (13), the total force applied to the haptic interface is
directly related to the magnitude of the gravity torque
The experimental process.
At this time,
Identification process of heavy torque.
When we choose Stribeck friction model, it contains four unknowns:
Flow chart of genetic algorithm.
Parameter identification process of friction model.
Genetic algorithm is an algorithm designed according to Darwinian evolution theory: through continuous natural selection, survival of the fittest, so as to obtain the most adaptable results (Liu, 2006). The process of parameter identification mainly includes generation of initial population, selection of race parameters, setting of fitness function, selection, crossover, variation and termination.
The search scope of parameters
The multi-group friction torques obtained through Eq. (18) can be expressed
as:
The minimum target value is defined as
The process of genetic algorithm is shown in Fig. 8, and its identification
process is shown in Fig. 9. Figure 10 shows the comparison between the
theoretical friction moment calculated by the identified parameters and the
actual friction moment. The measurement result of the friction torque at the
moment of
Curve of friction torque and rotational speed.
Parameter identification.
According to Eq. (14), the Stribeck friction torque model can be simplified
as:
Structural block diagram of motor driven haptic interface.
After sorting out Fig. 11, the simplified structure block diagram of motor driven haptic interface is shown in Fig. 12.
Simplified structure diagram.
According to Fig. 12, the continuous function can be expressed as:
Set the torque mode through the motor driver, set the specific current size,
and drive the haptic interface to rotate. When the motor speed reaches a
certain value, take multiple groups of current value
For the obtained data, the genetic algorithm in Sect. 3.2 can be used to
identify the moment of inertia. The estimated
The multiple groups of rotation angles
Identification process of moment of inertia.
Performming the same operation on the motor 2 as above, and the identified
moment of inertia
Based on the experimental platform in Fig. 2, the driver is connected to the
switch through the X11 terminal, and the switch is connected to the
computer. Use Visual Studio C
In this paper, the sampling time of the motor is given as 15 ms, and the
quadrature axis current
At this time, the driver's force on the haptic interface can be obtained through Eq. (13).
In the experiment, the pilot manipulates the haptic interface diagonally and nearly sinusoidal, as shown in Fig. 14a, and records the control force after the kinetic solution. The calculation result of haptic interface force in the whole process is shown in Fig. 14b.
Control process of the haptic interface approaching sinusoidal
motion.
Then take the take-off stage and the helicopter hovering to the left for example.
For the control process in the take-off stage, after lifting the total pitch
bar, the pilot slowly and uniformly pulls the haptic interface backward. The
haptic interface needs to be operated negatively along the
Helicopter take-off stage control process.
Helicopter hovering to the left.
For the control process of helicopter hovering to the left, the pilot slowly
and uniformly pulls the haptic interface. The haptic interface needs to be
operated forward along the
It can be seen from the experiments that the control process curve of take-off stage and left hover stage is consistent with the actual driving situation. It can be indicated that proposed identification method for the haptic interface model parameters are feasible and can be applied in the helicopter flight simulator.
In this paper we have addressed the dynamic modelling and parameter identification of a joystick-like haptic interface to be used for helicopter flight simulators. Careful attention has been addressed at the Stribeck friction model and its parameters for an accurate modelling of servomotors. A specific genetic algorithm has been implemented for an accurate identification of the Stribeck friction parameters. A full dynamic model has been developed and implemented as based on Lagrange formulation. Experimental tests show that the proposed identification procedure and haptic interface allow a control of both take-off and left hover stage with results being consistent with the actual helicopter driving. Accordingly, the proposed haptic interface can provide a reliable force feedback even without using expansive force sensors. As future work, we aim at improving the proposed model for a more accurate modelling of friction especially when the velocity is close to zero. Future activities will also include further experimental testing.
All data used in this paper can be obtained on request from the corresponding author.
DZ and JZ wrote the whole paper, HY and TN designed the experiment and dealt with data, GC and SY revised the paper.
The authors declare that they have no conflict of interest.
The authors would like to thank the Hebei Province “Giant Plan” (grant no. 4570031) and the Hebei Province Natural Science Fund (grant no. E2019203431) for supporting this research work.
This research has been supported by the Hebei Province “Giant Plan” (grant no. 4570031) and the Hebei Province Natural Science Fund (grant no. E2019203431).
This paper was edited by Daniel Condurache and reviewed by Adrian Pisla and two anonymous referees.