The human ankle is one of the most complex structures in the human musculoskeletal system and plays an important role in maintaining body balance during ambulation [32]. A pictorial view of the various bones and ligaments found at the foot and ankle are shown in Fig. 1.2. In general use, the term “ankle” is used to describe the structure which encompasses both the ankle and subtalar joints, where the ankle (or talocrural) joint is the articulation between three bones of the lower limb, namely tibia, fibula and talus. The subtalar joint on the other hand, is formed by the interface between talus and calcaneus and is located beneath the ankle joint.

Owing to its location, the human ankle is frequently subjected to large loads which can reach up to several times the body weight. The exposure to such large loads also means a higher likelihood of injuries. In fact, the ankle is the most common site of sprain injuries in the human body, with over 23,000 cases per day in the United States. In New Zealand, approximately 82,000 new claims related to ankle injuries were made to the Accident Compensation Corporation (ACC) in the year 2000/2001, costing an estimated 19 million NZD and making ankle related claims the fourth biggest cost for ACC [33].

Ankle sprains are injuries which involve the overstretching or tearing of ligaments around the ankle and are often sustained during sporting or physical activities. Ankle sprains can be classified into several grades, ranging from mild overstretching to complete disruption of ankle ligaments. Depending on the severity of the sprain, the time required for recovery can range from 12 days to more than 6 weeks [34]. Researchers have reported that a significant number (>40 %) of severe ankle sprains can develop into chronic ankle instability [35], which makes the ankle more susceptible to further injuries. Chronic ankle instability is thought to be caused by a combination of mechanical and functional instability at the ankle. Mechanical instability is used to refer to changes of the ankle anatomy which makes it more prone to future injuries, while functional instability refers to changes which give rise to insufficiencies in the ankle neuromuscular system, such as impaired proprioception, muscle weakness and reduced neuromuscular control.

The general rehabilitation programme for ankle sprains is carried out in stages as shown in Fig. 1.3. The initial stage of treatment right after injury is considered the acute phase of rehabilitation and is focused on reducing effusion and swelling at the affected to promote healing of the injured tissues. A reduction in effusion can be achieved with elevation, application of ice and compression. The affected ankle is also often immobilised. However, as prolonged immobilisation of the ankle can lead to reduced range of motion (ROM) and muscular atrophy, the next phase of ankle rehabilitation typically involve ROM and muscle strengthening exercises. With reduced effusion, the rehabilitation enters into the subacute phase where active and passive ROM exercises are normally carried out within the pain-free range of the patient to improve the range of motion and reduce muscular atrophy. Research has also suggested that this has the ability to stimulate healing of torn ligaments [35].

The rehabilitative phase is achieved once pain-free weight bearing gait is possible. During this phase, ROM exercises are continued together with the commencement of muscle stretching and resistive exercises [35]. The resistance level of these strengthening exercises should be increased as the patient progresses with recovery. Muscle stretching is important to assist the recovery of joint ROM while resistance training is used to improve the strength of muscles surrounding the ankle to prevent future injuries [36]. Finally, proprioceptive and balancing exercises should be carried out towards the end of the rehabilitation programme (functional phase) to enhance the patients’ sense of joint position, thus giving them better foot and ankle coordination and improving their ability to respond to sudden perturbations at the ankle [35].

As can be seen from the previous discussion, muscular strength and good proprioception are vital in preventing functional instability in the ankle. Emphasis must therefore be placed on these areas and an extensive rehabilitation programme is needed to minimise the likelihood of recurrent injuries. The repetitive and tedious nature of such exercises therefore makes robotic devices an attractive alternative to manual manipulation. However, the great variability observed between different patients due to either their level of injury or their ankle characteristics such as joint limits and stiffness also means that any robotic device employed in this area must be adaptive to allow it to cater for the requirements of specific patients.

Traditionally, many robotic devices are position-controlled and various mature control techniques had been developed for the design of position controllers. However, when robots are deployed in applications that require significant physical interaction with the external environment, pure position control is no longer adequate [37]. This is because the design of the position controller is normally done by considering the dynamics of the robot alone and treating externally applied forces/torques as disturbances. However, when the robot comes into contact with an external environment, the assumed robot model may no longer be valid and the robot will therefore deviate from its intended behaviour. Furthermore, as large controller gains are normally used in position controllers to minimise position-tracking errors, interaction with a stiff environment will result in large position errors which can in turn lead to force build up at the contact interface. This is of course unacceptable for robots which interact closely with humans as it is likely to cause injuries to the user. Clearly, a control strategy which takes more than just position into consideration is needed for the control of rehabilitation robots. Interaction control is an approach which aims to regulate both the forces and the motion of a robot which is in contact with an external environment. Two groups of interaction control schemes are commonly used. They are hybrid force-position control and impedance control [34, 38].

Hybrid force-position control [39] is a control strategy which splits the task space into two complementary subspaces using a selection matrix. A position control strategy is then applied in one of the subspaces and a force control in the other. Normally, directions where constraint-free motion is permissible are position-controlled while force control is applied in the constrained directions. This will allow accurate realisation of the desired force and motion when the kinematic constraints in the environment are known with little or no uncertainty. While such constraints may be well known in an industrial setting, there can be considerable variations in the joint kinematics of different individuals. This would mean that hybrid force-position control may still result in large interaction forces due to imprecise definition of the free motion directions. Furthermore, if the robot were to move from a constraint-free state to a constrained state, a switch in the control law is required since all directions need to be position-controlled prior to contact and the hybrid position-force control should only be active after contact has been made.

Impedance control is another type of interaction control scheme which aims to maintain a prescribed relationship between force and motion of the robot. This relationship is termed the mechanical impedance and is defined as the dynamic ratio of the error in applied forces to the velocity error of the robot end effector. Consequently, unlike the hybrid position-force controller, no switching of control law is required for impedance control [38].

Selection of the target manipulator impedance is an important issue in impedance control as it establishes the physical behaviour of the controlled manipulator. For a single-input-single-output system, it can be seen that an infinite impedance will result in pure position control while a zero impedance will lead to pure force control. From this observation, impedance control can be designed to give a similar performance as hybrid position-force control by selecting larger impedance values in directions of free motion and smaller impedance values in constrained directions. While the selection of target impedances can be achieved through experimental trial and error, more systematic approaches can also be taken. Researchers have suggested that the choice of impedance parameters should be based on optimisation of certain objective functions. For instance, the target impedance can be chosen to be proportional to the environmental admittance to minimise a weighted sum of position error and actuator force [40].

It is evident from the above discussion that impedance control is a more robust interaction control scheme than hybrid force-position control. It is therefore not surprising that a large proportion of rehabilitation devices have employed some form of impedance control to deal with the variability found among patients [41–44]. However, a more robust nature of impedance control does not mean that knowledge of the operating environmental is no longer important. Information of the environmental dynamic characteristics can be used to alter robot behaviour in such a manner that the robot performance can be enhanced. The ability to adapt the impedance controller according to changes in environmental conditions is therefore a desired feature in rehabilitation robots.