# Foot-Mounted Inertial Measurement Units-Based Device for Ankle Rehabilitation
## 1 Introduction
An example of these systems is the Biodex Multi-Joint System 4 Pro [1]. Besides the lack of portability, perhaps the most important disadvantage is that intermediate and complex systems work in a continuous passive motion basis [1,3,4]. This reduces the type of therapy where they can be used. Portable devices are needed for the active rehabilitation of ankle injuries; these devices could reduce the cost of healthcare for patients [5]. Inertial measurement units (IMU) can be used to make portable rehabilitation devices. They have been extensively used in position and attitude estimation, allowing for pedestrian navigation tracking [6, 7, 8, 9, 10, 11, 12, 13], gait analysis [14, 15, 16, 17, 18, 19, 20], foot pose estimation [21], foot clearance estimation [22], wearable devices for Game Play application [23], and detecting foot strike in recreational runners [24]. A problem of inertial measurement units is that they present biases and other systematic errors that are responsible for position and attitude estimation errors. To provide robust distortion-free and refined absolute position and orientation vectors, data fusion is used to combine the measurements from the three-axis gyroscope, three-axis geomagnetic sensor, and three-axis accelerometer enclosed in the IMU [17]. Approaches used with data fusion include Kalman filters [6,9,15], clustering algorithms [7], and hidden Markov models [8]. Some of these approaches rely on additional information, such as map information [8,10], multiple IMU [11], biomechanical models [25], or light detection and ranging (LIDAR) systems [12]. A major challenge of micro-electro-mechanical systems (MEMS) position estimation concerns how to restrain the rapid accumulation of navigation errors. Without an error-resetting algorithm, this error rapidly increases. For pedestrian navigation tracking and gait analysis, a zero velocity update (ZVU) algorithm could be employed as an effective way to correctly detect the stance phase of each gait cycle and compensate for speed bias errors [6; 9]. Another source for errors in IMU sensors comes from magnetic disturbances that might take place in indoor environments such as medical facilities, which becomes a problem for IMU clinical applications. Two approaches that are used to reduce the impact of magnetic disturbance are: magnetic anomaly detection algorithms [13], and a method based on analytical solutions in combination with parameterization for corrections [26]; both are used as part of data fusion. IMU use related to rehabilitation therapy can be separated into systems that provide explicit biofeedback for therapy and those that aim to help with the diagnosis and detection of pathologies. In the first group, we can find systems for treating foot drop syndrome [27], hip and knee rehabilitation exercises [28], improving therapy adherence [29], improving gait in patients with walking disabilities [18], exoskeletons [30], and even therapies for animals [20]. In the second group, we can find systems that help diagnose gait pathologies [16], explore elderly gait [19], and assess human gait parameters [14]. Most of the above used foot-mounted devices or insoles. [PERSON], [PERSON], [PERSON] [18; 27; 30] created systems that depend on other sensors besides the IMU. [PERSON] [28] tested their system with a single IMU mounted on the foot and another IMU incorporated in knee and hips, and [PERSON] [29] used a single IMU-based approach as well. The case has been made that for some rehabilitation, a single IMU could suffice for posture and motion recognition [28]. Of relevance is [PERSON] [27], which explored foot movement for rehabilitation, and used IMU to map foot pitch and roll to dorsiflexion, version, and inversion movements, which are also used in rehabilitation exercises for ankle strains. In this paper, we developed a foot-mounted inertial sensor device to determine the foot attitude with the aim of making an active rehabilitation session following the same process that a therapist would.