Human postural ankle torque control model during standing posture with a series elastic muscle-tendon actuator

Research Article Human postural ankle torque control model during standing posture with a series elastic muscle‑tendon actuator Mohammad Javad Fotuhi1 · Orkun Yılmaz1 · Zafer Bingul1 Received: 2 November 2019 / Accepted: 3 January 2020 / Published online: 18 January 2020 © Springer Nature Switzerland AG 2020 Abstract The main motivation behind the creation of a compliant actuation system is to provide safety, capability of storing energy, and improved performance levels in dynamic behavior of the mechanical human ankle. In this paper, a torsional flat spring (TFS) is proposed to provide high compliance and deformation values for human ankle series elastic muscletendon actuator system (HA-SEMTAS). The proposed torsional flat spring uses two torsional flat spiral spring in opposite directions, as the torsional flat spiral spring generates torque only in one direction. First, we present the characteristics of the TFS for an ankle joint, and the design and modeling of the HA-SEMTAS are developed. Modelling of the HA-SEMTAS simulates the responses of fluctuations in the center of mass and center of pressure and offers the possibility of measuring sensor activation, decomposition of reactive torque and participation of each set of muscle groups to balance posture. In order to control ankle angles and torque of Human system, torque controllers (PID and PD-feedforward) are generated for (HA-SEMTAS). The controller inputs are torsional flat spring position errors and error rates. Feedforward and integral action were applied to reduce the steady-state error of the system. It is seen that PID + ff of the system developed here is robust to step and ramp-type disturbances. Real-time controllers are embedded in GoogolTech GT-800 Industrial PC. Experimental results confirm that the step tracking of human upright posture behavior is satisfactory and overall system stability has improved using the proposed controller and compliant actuation system. It is also shown that PD + feedforward yields better performance than PID controller. Keywords Series elastic actuator · Postural control · Ankle strategy · Pd-feedforward · PID 1 Introduction Human stability related diseases are becoming more common with the increase in the average age of the people [1, 2]. With ageing, risk of falling in daily life inevitably increases. These falls can cause various injuries like cracks and fractures in elderly people. This type of injury reduces the quality life. Furthermore, even if these injuries can be treated, some complications after surgeries can be dangerous. Studies about postural stability are vital to gain more understanding about self-balance mechanisms of the human body. Postural stability can be defined as the ability to adjust the displacement of the body’s centre of pressure (CoP) to react to the movement of the centre of gravity (CoG). Internal and external disturbances that more dynamic than body’s reaction time can cause to fall. In order to work on postural control, various systems were created in previous studies. After studying the literature, two basic and different perspectives can be found for bipedal posture control. One of them is biologically inspired (BI) approach which can be called sensory-based approach. Humans process the data collected from vestibular system, muscle spindles (proprioceptive) and force * Mohammad Javad Fotuhi, ; Orkun Yılmaz, ; Zafer Bingul, | 1Robotics and Automation Laboratory, Mechatronics Engineering Department, Kocaeli University, Kocaeli, Turkey. SN Applied Sciences (2020) 2:229 | https://doi.org/10.1007/s42452-020-1955-5 Vol.:(0123456789) Research Article SN Applied Sciences (2020) 2:229 | https://doi.org/10.1007/s42452-020-1955-5 sensors to control their balance. BI approach has been developed based on this knowledge and a multi-sensory system is used for estimation of CoG’s position and orientation values and compensation of disturbances in order to control balance [3, 4]. The other widely used viewpoint is the robotics approach which is a model-based method. Unlike the BI in this approach, a dynamic model of the body is required. In [5–7], model-based bipedal control systems were developed. Morphological reconstructions are commonly used for decreasing the complexity of the dynamic model without distorting biomechanical behaviors. Since ankle joint performs the most effective task of maintaining equilibrium in sagittal plane, a simplified single inverted pendulum model (SIP) can be substituted over the exact model in lower extremity bipedal balance problems [8]. In this study, we designed and built a lower extremity system to work on the postural stability control in the sagittal plane. The main difference of the proposed system is the series elastic actuator we added to ankle joint that named as human ankle series elastic muscletendon actuator (HA-SEMTAS). Since elastic series actuators are similar to skeletal muscles’ structure, their use in the system resemble the response more like human [9]. HA-SEMTAS consists of a torque motor with two encoders (one of them is directly connected to the motor shaft and the other one is on the output shaft), a worm gear, a spring. Another contribution of our study is the design of Torsional flat spring. In order to change the stiffness of HA-SEMTAS, various types (thickness, materials) of these springs are manufactured. The rest of our article was created as follows. In Sect. 2, the mathematical model of HA-SEMTAS is presented. Section 3 presents the control engineering framework, describes its main features and discusses how they are compared to those of the biological analysis. In Sect. 4 postural controller design is shown. Finally, Sect. 5 gives the main conclusions. 2 Material and methods • Torsional flat spring • Incremental encoders • Link and joint of the ankle The torque motor model is LFTM-50, which has a highresolution encoder. The rotary motion of the torque motor is converted to the other axis motion by a worm gear with the use of the bullring. The well of worm gear mechanism is connected to the link of ankle case and transmits the motion to the carriage where torsional flat spring is placed between them. The transmission ratio of the motor and worm gear system is 1:60. The spring constant is 63.665 Nm/rad and has a working stroke of 1 rad. The designed system is shown in Fig. 1. For the adaptation of the elastic tendon actuator (Fig. 1), it is assumed that the elastic elements integrated in the tendons can be approximated as massless springs. This assumption is valid if the springs’ mass is small compared to the effective mass of gearbox inertia and the motor and the effective mass of the joint and attachment. In the case of motors, this is especially true when using high reduction ratios gearboxes. The effective mass of the link is normally also higher by at least one magnitude. Figure 1 shows an overview of important parameters and variables of the series elastic muscle-tendon a (...truncated)