*2.3.1. Control of passive mobilisation cycles*

98 Smart Actuation and Sensing Systems – Recent Advances and Future Challenges

*2.2.3. Choice of the SMA element* 

temperatures as provided by DSC analysis will be shifted when the material is loaded. Typical values of *C* for NiTi range from 5 to 9 MPa/°C, i.e. an actuator designed to bear 200MPa would have transformation temperatures increased by as much as 40°C. However, actuation temperatures cannot be increased indefinitely: in fact, above a certain temperature (*Md*), part of the deformation cannot be recovered and material undergoes plastic slip.

SMA actuators can be provided in a number of shapes, which may differ significantly from one another in terms of available stroke and force. The first distinction is based on the deformation mode imposed onto the material. Wires are subjected mainly to traction, which produces a uniform loading of the material cross-section: this fact makes it possible to produce high force actuators, but, on the other hand, the available stroke is limited by the fact that linear deformation can be as high as 8% only, 4% in most cyclic operating modes. Other simple SMA actuators are linear springs (tension or compression springs), whose principal mode of deformation is torsion. Springs of this kind are helical coils of SMA wire arranged around a central axis: this allows for large elongations along the central axis depending on spring ratio and the number of turns. On the contrary, force is limited by the fact that torsional loading is not uniform in the material cross-section. Some authors proposed also bending actuators, made of SMA ribbons [27] or SMA wires [33]. For the same purpose, also torsion springs and flat springs can be employed, which share the same principal mode of deformation, i.e. flexion. The advantage of this actuation is that angular stroke is directly

available, but the non-uniform cross-section loading limits the available torque.

requirements for actuation, keeping in mind also the safety issues.

**2.3. Actuator control** 

The problem of moving human joints generally involves large angular strokes coupled with fairly high levels of force or torque. The simple configurations just described most of the time provide solutions only for very long wires or thick cross-section springs, ribbons or bars, which are often deemed impractical for a number of reasons. Long wires have to be housed in a suitable manner, to limit length into a compact three-dimensional structure. A way to do so is coiling the SMA wire along a series of pulleys, whose diameter should be sufficiently large with respect to the wire diameter, to avoid strain concentrations. On the other hand, large cross-section actuators are impractical because they need high electric power to reach the transformation temperature. Moreover, cooling down bulky wires or ribbons may require too long a time for most cyclic applications. A possible solution for increasing force output in springs and ribbons is arranging many actuators in parallel or in bundles. Provided space around the joint is sufficient, attention should be posed to electrical insulation and electrical connections, in order to provide suitable solution to tension-current

The problem of controlling actuation is very important for many applications in Rehabilitation, as patient's needs and responses may vary during the evolution of therapy or even during the same session of exercise. Control strategies apply mainly to assistive robots, Two major strategies exist to control cyclic heating and cooling of SMA actuators: in *openloop control* parameters are predetermined by a set routine, whereas *closed-loop control* employs a feedback signal of any nature to adjust heating and cooling parameters (timing, current or voltage, active cooling systems, etc). The main drawback of open-loop control is that any perturbation to the trajectory would not be compensated, as the current profile is predetermined. This could happen, for example, if patient exerts any unexpected active contraction or in the case of unpredicted changes in environmental conditions. However, there are applications in which open-loop control is still feasible, for example repetitive passive motion of flaccid limbs. Closed-loop controls need monitoring of a feedback variable, which could be the SMA temperature, the joint angle, actuation speed, SMA force or any other measurable physical quantity. Apart from rare examples of feedback loops based on monitoring of SMA resistance [59], closed-loop controls rely on dedicated sensors that are better included from the initial steps of the device design.

Another distinction can be made on different types of control of movement trajectory. In many applications an ON/OFF actuation is suitable: the focus is only on the initial and final positions, while the detailed trajectory is controlled only mechanically and the speed only in average terms. In this case, open-loop control may be practical, and heating can be achieved with a very simple current profile, e.g. a step or a ramp. Experimental tests are a viable solution to adjust the heating and cooling parameters. In particular, attention should be paid to the experimental conditions, including the orientation of the actuator in the gravitational field, as thermal convection is strongly dependent on that.

On the other hand, when a precise trajectory of movement over time is required for the application, alternatively open-loop or closed-loop control strategies can be applied. In the open-loop approach, Equation 1 should be solved by imposing the desired mechanical output *W*(*θ(t),t*) and by calculating the time-varying current profile to be injected. However, the most reliable way to provide trajectory control is closed-loop control, in which the current input is continuously adjusted to match the prescribed position, thus counterbalancing perturbations.
