Over the past sections, a number of tunable parameters were mentioned that will determine the behaviour of the designed controller. This section will detail the design choices that were made regarding the quantification of these parameters. An overview of all parameters that are used throughout this research, unless explicitly indicated otherwise, is presented in Table 4.2.
Parameter Value Parameter Value Parameter Value
Kv,mi n 100 [N/m] Dv,mi n 0.2 [N·m·s/rad] Hd 0.1 [J]
Kv,max 600 [N/m] Dv,max 0.5 [N·m·s/rad] γ 200 [N·s/m·J]
Kv,r ot 100 [N·m/rad] ωl oop 1000 [Hz] β 0.01 [−]
Kv,d i s 1000 [N/m] ωc,l p 5 [Hz]
Table 4.2:Recommended parameter settings. These settings were used throughout this research, unless explicitly indicated otherwise.
Setting the impedance parameters is mostly a matter of tuning. Creating the desired beha- viour does not only depend on the dynamic properties of the robotic devices and the human operator but also on their respective configurations. Furthermore, it is hard to quantify the feeling of the operator when determining the quality of the haptic feedback. For these reasons, the minimum stiffness level of the controller (Kv,mi n) was empirically determined at a value of
100 [N/m], such that a minimum allowable level of interaction control was achieved. With this setting, low frequent motion tracking and a limited but distinguishable sense of touch were achieved, of course still depending on the circumstances.
As for the maximum stiffness levelKv,max, the upper boundary is a bit more clear. For motion
tracking, only relatively low frequencies (say, up till 5 [Hz]) are of importance, since higher fre- quencies will never be commanded by a human operator and might only cause a disturbance. However, increasing the stiffness as much as possible might be beneficial for accurate haptic feedback of the robot’s interactions. Here, the limiting factor will be a result of active behaviour of the impedance controller. Although the stability layer will make sure the system remains stable, a large amount of energy leakage will still cause some resonance behaviour plus the ad- ded damping by the TLC might decrease the transparency level. As a benchmark, an absolute upper bound is determined at 1000 [N/m]. With this setting, the most important motions of the
human arm (in a range of 0−3 [Hz]) will quickly be tracked by the slave arm, assuming the equi- valent moved mass will be equal to 5−10 [kg] of the total 16 [kg]. Initial testing however showed that, due to the relatively high inertia of the simulated robotic arm and the additional frictional properties found in the real KUKA arm, the arm behaves as quite a slow object causing high controller efforts which quickly results in large amount of energy leakage. Limiting this beha- viour can be achieved most effectively by tuning down the stiffness level of the controller and decreasing the time delay of the communication. Throughout this research, a maximum time delay of 10 [msec] will be used, in combination with a maximum stiffness ofKv,max=600 [N/m].
This was empirically determined to still give satisfactory transparency properties due to limited necessary intervention by the stability layer, while the effects of time delayed communication still become apparent. In case a more lightweight robot would be used with lower overall fric- tional properties (a robot with better transparency properties, i.e. dynamics that can more easily be assumed negligible), communication with larger time delays is expected to be less of a problem.
The other stiffness settings, Kd i s and Kr ot, are not used while interacting with the master
device, so these controllers are not subjected to communication delays. This makes it easy to establishKd i sat the benchmark of 1000 [N/m].Kr ot is established at 100 [N·m/rad], since the
moment of inertia of the KUKA can be assumed to be much lower than its mass properties regarding its dimensions.
Chapter 4. Design 43
The desired amount of joint damping cannot easily be related to these stiffness values be- cause of the conversion between Cartesian and joints space and the dependency on configur- ation and unknown dynamic characteristics of the devices. Because of this, the joint damping settings were chosen equal for each joint while quick experimenting with impacting objects showed the damped behaviour of the impedance controller’s oscillations. The damping values were tuned at 0.2 and 0.5 [N·m·s/rad] forDv,mi nandDv,maxrespectively.
Quantifying suitable stability layer properties is not trivial either, because of large dependency on the characteristics of the systems, controllers and communication channel. With the im- pedance settings quantified and the time delay limited to 10 [msec], suitable settings are first estimated and then tuned empirically. The minimum tank level,Hd, should be chosen such
that there is a bit of an energy buffer such that the controller also runs smoothly with the added communication delay. The upper bound will be defined by the amount of energy that is allowed to be translated into active behaviour. It was experimentally determined that a value of 0.1 [J] resulted in smooth functioning of the controller for the circumstances tested in this research. This value is assumed to not cause dangerous levels of active behaviour, since this amount of energy can be interpreted as the amount of kinetic energy that the slave robot would posses while travelling at about 0.1 [m/s].
The parameter quantification of the damping parameterγis hard to determine analytically as well, since it highly depends on system characteristics, the implemented energy transfer pro- tocol and the time delays in the communication channel. Its value should guarantee stability while not disturbing the user too much which would be the case during aggressive damping. As an indication, it was assumed that an allowable damper force should not exceed 2 [N], which would be about one fifth of the maximum force application by the master device. For a tank level of 0.1 [J] and a maximum velocity of the master device of 0.1 [m/s], this would come down toγbeing equal to 200 [N·s/m·J]. This parameter setting was tested and proved to guarantee stability under the conditions tested in this research while not disturbing the user too much. The final parameter that is part of the stability layer isβ. This value partly determines the successfulness of the energy transfer protocol that balances the tank levels. A value ofβ=0.01 was experimentally determined to show satisfactory results, meaning that at every iteration one percent of the levels of each tank is send through the communication channel.
Finally, the corner frequencyωc,l pof the low-pass filter used on the muscle activation signals
was set at 5 [Hz], which was already discussed in Section 4.1 of this chapter. The loop frequency
ωl oopwas set at 1000 [Hz] which was empirically determined as a maximum rate at which the controller could smoothly function on the used hardware.