Introduction

Haptic systems are designed for the interaction between a virtual tool in a simulation situation computing [Corrêa 2019], to teleoperate a remote robot (carrying a haptic probe, for example Krupa 2014], or a UAV flotilla [Son 2019], ...
For educational purposes, the behavior of such systems must be realistic (also closer than the tool they simulate), but off-the-shelf haptic systems are not always suitable [Kheddar 2004].

For some practical reasons, commercial simulators are equipped with electric actuators which provide feedback imitating, for example, the behavior of a tool touching a human organ in a surgical context.
Today, the haptic control laws applied to electric actuators are well mastered.
However, electric actuators have certain limitations for this type of use:

• they have a lower power-to-weight ratio than pneumatic actuators;
• it is difficult for them to provide a high torque at high speed;
• they need reducers (which limits their reversibility), and;
• they heat up when low-speed torque is required.

All these limitations reduce their performance when it is necessary to reproduce a variable stiffness quickly.
For several decades, complex mechanisms have been devised with the aim of providing compliance to actuators: these are called “Variable Stiffness Actuators – UAV ”. These actuators independently control their balance position and stiffness. Van Ham et al. present a state of the art on VSAs [Van Ham]. Most of them are designed with two opposing electric motors and passive compliant components. One of the advantages of this approach is that the control of position and stiffness are obtained independently by controlling the position of each motor. The main disadvantages are their cost (two motors per axis) and the limited amplitude of the stiffness due to the use of passive components [Huang 2013].

Shortly before my arrival at the Ampère laboratory, due to a long-standing expertise in action control, pneumatic actuators, the medical robotics team had begun to take an interest in the use of such actuators to render a haptic rendering. This technology is underused at the industrial level because it is considered too complex to control. However, it brings new possibilities in the medical field. In fact the actuators tires have a very interesting structural compliance. Simultaneous pressure control in both chambers of a cylinder opens the way to control of the mechanical stiffness of the piston and therefore to a rendering in effort of better quality than that obtained with electric actuators. At equal and constant pressure at rest in each chamber of a jack, this one, during an excitation, will react like a spring presenting a stiffness during the initial pressure level. With an electrical system, it is necessary to enslave the motor to recreate this natural phenomenon. On the other hand, by adjusting the pressure difference in each chamber, it is possible to check the pneumatic force applied to the piston. In summary, the advantages of pneumatic actuators over electric actuators are:

• a higher force-to-mass ratio;
• the non-necessity of a reducer;
• their ability to be powered by energy readily available in industrial and medical environments and sufficient
  sufficiently clean (provided it is filtered) for biomedical applications;
• the possibility of being non-magnetic, which allows them to be used in environments such as an MRI.

However, pneumatic actuators have a major drawback: the air is compressible and the behavior of pneumatic actuators is inherently non-linear. Unlike hydraulic actuators, dry friction is important since air is a low viscous fluid.

Contributions

In 2011, when I arrived at the Ampère laboratory, a research project concerning the teleoperation of robots using pneumatic actuators had been started. Indeed, it turned out that many works dealt with the modeling of pneumatic components (actuators, power modulators) but also their control with a view of position or force control [Belgharbi, 1999], but very few concerned their use in teleoperation. In the framework of of Minh Quyen Le's Ph.D., the team had developed a pneumatic haptic interface that could accommodate two types of power modulators: proportional servo valves or solenoid valves. The servo valves deliver an air flow depending on the control voltage and downstream pressure, while the control of solenoid valves is limited to open or close.
In the industrial world, despite their performance, servo valves are much less widespread than solenoid valves because of their price but also the expertise needed to fully exploit them. A modeling had been proposed and a control architecture produced using a linear tangent model of the pneumatic and mechanical chain around an operating point. This model resulted in a transfer function of the third order (integrator + second order) which has been used in a four-channel teleoperation architecture.
Experiments led to interesting results.

However, additional experiments, which I conducted personally upon my arrival, showed that this control architecture did not make it possible to correctly control the pressure levels in the cylinder chambers, resulting in under-performance. Typically, cylinder chambers were often at average pressure levels close to the intake pressure (therefore at the maximum), which prevented to efficiently and quickly generate pneumatic forces as it was necessary to wait for one of the chambers to empty the air, to generate this desired force. Maintaining the chambers at an intermediate pressure would have made it possible to play simultaneously on the pressurization of one chamber and the depressurization of the other and to gain in dynamics.
On the other hand, for our haptic applications, the choice of servo-valves available on the market is limited because the latter are mainly dedicated to more powerful industrial applications and are poorly suited to low forces and small displacements encountered in our case. For all these reasons, the team had simultaneously decided to study the use of solenoid valves. Unlike proportional servo valves, there is a range largest number of off-the-shelf solenoid valves. These components have an on/off type operation which more coarsely modulates the useful air flow. By playing on the rapid switching from closing to the opening (and vice versa) of the solenoid valves, the team sought to control the flow of air sent to the rooms pneumatic actuators (and the exhaust flow from them). It was therefore an approach of control of a hybrid system: switching and non-linear dynamics.

For my part, I participated in the development, optimization and experimental validation of the integration control laws developed by the team for a pneumatic actuator in a teleoperation loop with only one degree of freedom.

Two control approaches have been proposed, tested and compared. This work has been published in two international journal articles [Hodgson 2014a] [Hodgson 2015] and two international communications [Hodgson 2012] [Hodgson 2014b].