Hybrid Modeling and Fractional Control of a Sckafo Orthosis for Gait Assistance

SCKAFO, stance-control knee-ankle-foot orthosis, is a type of orthosis that permits free knee motion during swing while resisting knee flexion during stance, supporting thereby the limb during weight bearing. This orthosis specially assists patients who have incomplete spinal cord injury and allows them to walk with the aid of canes or crutches, maintaining a proper gait. In this paper, based on the human walking biomechanics, the SCKAFO hybrid modeling is proposed, which consists of eight different stages whose evolution is given by means of four planar sensors on each foot. In the model, it is considered that the patients can move their hip but not their knee that will be controlled using a DC motor. Two fractional order controllers are designed, following decision based control techniques, to control the knee angle. Simulation results are given in order to demonstrate the efficiency of the system performance. INTRODUCTION Spinal cord injuries cause paralysis of the lower limb in a major or minor degree based on the height of injury on the spinal cord. Incomplete spinal cord injured subjects can perform a high metabolic cost and low speed walking aided by crutches, bars or similar. In the literature, several devices have been proposed for assisting human gait to improve their walk. A survey on the current state of the art of such devices can be found in [1]. Indeed, the particular characteristics of the orthosis are based on the type of injuries, which will define a specific design process. For example, a biologic-based design is described in [2]. The stance control of the orthosis is a fundamental part of the design of the orthosis (refer to [3] for a review of this issue). Control tasks are necessary to identify gait cycle and establish locking and actuation stages. The design of the control will define the locomotor adaptation as is exposed in [4]. Fractional order controllers have received a considerable attention in the last years both from an academic and industrial point of view [7–11]. In fact, such controllers provide more flexibility during the controller design than the classic ones. The aim of this paper is twofold. On the one hand, a hybrid model of the system operative is proposed based on the use of planar sensors located in the foot. In addition, the orthosis separates mechanical actuation and locking system on the knee, which allows reducing actuation requirements, and, consequently, the weight of the device. On the other hand, a fractional order controller is designed to control the knee angle, whose dynamics is based on the motor and load (orthosis) model. In addition, regarding to human walking biomechanics, a linear reference is proposed for each stage. The rest of the paper is organized as follows. Biomechanics of walking is presented in the next section. Then, the reference for the knee angle is introduced. After illustration of mechanical design of the SCKAFO the control design is presented. Finally, the paper will be concluded with some remarks. BIOMECHANICS OF WALKING The gait cycle is defined as the time interval between two successive occurrences of one of the repetitive events of walk1 Copyright c © 2011 by ASME ing. Although any event could be chosen to define the gait cycle, it is generally convenient to use the instant at which one foot contacts the ground (’initial contact’). If it is decided to start with initial contact of the right foot, then the cycle will continue until the right foot contacts the ground again. The left foot, of course, goes through exactly the same series of events as the right, but displaced in time by half a cycle. There seven major events (Initial contact, Opposite toe off, Heel rise, Opposite initial contact, Toe off, Feet adjacent, Tibia vertical) that subdivide the gait cycle into seven periods, four of which occur in the stance phase, when the foot is on the ground, and three in the swing phase, when the foot is moving forward through the air. The stance phase is also subdivided into: 1. Loading response, 2. Mid-stance, 3. Terminal stance, 4. Pre-swing. The swing phase lasts from toe off to the next initial contact. It is subdivided into: 1. Initial swing, 2. Mid-swing, 3. Terminal swing. The duration of a complete gait cycle is known as the cycle time, which is divided into stance time and swing time. In the stance phase the controller will lock the motor not to move and let the patient control his knees. And in the swing phase the controller will adopt himself to follow the reference. Fig. 1 shows when the controller should lock the motor (stance) and when the controller has to follow the reference (swing). In the double stance, both knees are locked. FIGURE 1. Timing of single and double support Likewise, Fig. 2 shows a simplified diagram of human walking gait, with the terms that will be used. Fig. 3 shows the sagittal plane angles at the hip and knee joint for the right leg showing joint angle for hip and knee FIGURE 2. Biomechanics of walking áexion/extension motions during level-ground walking. These data are achieved for the right leg in a gate cycle [6]. FIGURE 3. Sagittal plane joint angles (degrees) during a single gait cycle of right hip (aexion positive) and knee (aexion positive). IC = initial contact; OT = opposite toe off; HR = heel rise; OI = opposite initial contact; TO = toe off; FA = feet adjacent; TV = tibia vertical. HYBRID DYNAMICS OF ASSISTED GAIT To control an orthosis to introduce an applicable reference is necessary. Therefore, four planar sensors will be used in the orthosis to find periods and then a linear reference will be introduced for each period. Planar sensors are ON/OFF sensors where 1 means that the leg is in touch with the ground and 0 refers to the contrary situation. Using the planar sensors and based on the human walking biomechanics (see Fig. 2) we will see eight different parts in each gate cycle of walking. The activation of the sensors in each part is shown in Table 1. In this table, P1 to P8 represent part 1 to 8 and PS1 to PS4 refer to each planar sensor. 2 Copyright c © 2011 by ASME Concerning those eight parts, seven periods for both legs can be achieved. Table 2 shows the relation of both legs in each part. TABLE 1. Planar sensor configration in each part PS1 PS2 PS3 PS4 P1 Right 1 0 0 0 Left 0 0 0 1 P2 Right 1 1 0 0 Left 0 0 0 0 P3 Right 1 1 1 0 Left 0 0 0 0 P4 Right 1 1 1 1 Left 0 0 0 0 P5 Right 0 0 0 1 Left 1 0 0 0