Smooth Trajectory Planning for a Cable Driven Parallel Waist Rehabilitation Robot Based on Rehabilitation Evaluation Factors

In recent years, with the increasing trend of social aging, the number of stroke patients has increased accordingly [1]. The symptoms of waist impairments commonly occur in stroke patients. Research on modern rehabilitation medicine and neuroscience show that task-oriented repetitive movements can improve muscle strength and coordination in patients with motor dysfunction [2]. With the help of rehabilitation robots, patients can regain the ability of waist movement through repeated gait, sit-up or waist-twisting training [3, 4]. Due to the interaction between rehabilitation robots and patients, the robots need to complete rehabilitation training on a safe basis [5, 6]. The effect of waist rehabilitation is related to some factors, such as the intensity of rehabilitation training and the flexibility of rehabilitation movement. Therefore, the rehabilitation trajectory should be designed based on the motion of human waist.

To develop rehabilitation robots and training trajectories more suitable for patients, research on human motion models has been carried out [7]. It is found that the complexity of human motion cannot be simply defined as a combination of several degrees of freedom, which deviates from the real needs of rehabilitation patients [8‐10]. Varela et al. [11] proposed a cable-based parallel manipulator system CaTraSys to measure the kinematic characteristics of human walking. Hu et al. [12] considered the rotation of human waist and estimated the human walking speed using a wearable accelerometer. Martín et al. [13] detected and identified six postural transitions using an inertial sensor located at the human waist. The cross-section average method is widely used in the time alignment processing for data series to reduce the impact of movement variability in the human body, which eliminates the inherent change characteristics of the data and ignores the drift of the center point to a certain extent [14].

The collected information on human motion is essentially a series of discrete position points, which needs further trajectory planning. The trajectory planning problem in 3-D space contains point-to-point trajectory planning with determined initial and end points, and multi-point trajectory planning by interpolating or approximating a set of via-points [15‐18]. In point-to-point trajectory planning, polynomial, cycloid, and trigonometric function curves are commonly used to define trajectories [19]. Each segment can be optimized separately to obtain specific kinematic characteristics. Multi-point trajectory planning is a global optimization problem [20‐23]. The approaches mainly include polynomial functions of proper degree and B-spline functions. Gosselin [24] presented an approach for dynamic trajectory planning of 3-DOF spatial cable-suspended parallel robots using periodic functions, which can guarantee that cable tensions remain positive throughout the trajectory. Jiang et al. [25] conducted point-to-point dynamic trajectory planning for a 6-DOF cable-suspended parallel robot, which can generate the trajectory beyond the static workspace of the robot. Li et al. [26] presented an approach for smooth trajectory planning of a 4-DOF SCARA using quintic B-splines to achieve C4-continuity. Abbasnejad et al. [27] designed a 4-4 planar cable-driven parallel robot for gait rehabilitation and optimized the gait trajectory with the particle swarm algorithm.

In summary, the current research on human motion models is mostly related to the gait characteristics in normal walking, running or abnormal walking, and the research on motion characteristics in waist twisting is relatively limited. In addition, due to the interaction between rehabilitation robots and the human body, the motion trajectory needs to ensure compliance based on the safety and comfort of patients. Therefore, the mentioned trajectory planning method needs further study.

In this paper, an approach for smooth trajectory planning for a cable-driven parallel waist rehabilitation robot (CDPWRR) based on the rehabilitation evaluation factors is proposed. Considering the impact of movement variability, the feature points at the center of the human pelvis are obtained after collecting and processing waist motion data. The prototype of the CDPWRR is built, and the feasibility of the proposed method is verified by numerical analysis and experiments. This paper is arranged as follows. In Section 2, the waist motion data of several male adults in waist twisting are collected, and the waist feature points are obtained. In Section 3, the waist training trajectories are generated by the quintic polynomial, cycloid and quintic B-spline functions, respectively. In Section 4, the rehabilitation evaluation factors are introduced, and the smooth trajectory planning for waist training on the CDPWRR is conducted. Subsequently, the feasibility and effectiveness of the proposed method are verified on the physical prototype. Conclusions are drawn in Section 5.

20 male adults are chosen as the volunteers, and the Nokov optical motion capture system mainly composed of 8 infrared cameras is used to capture the motion data of the human waist [28]. 4 markers are evenly placed at the waist of volunteers, which are located at the front, back, left and right directions, respectively. The joints of upper and lower limbs are used as auxiliary points. Before the experiment, volunteers need to perform the slow counterclockwise rotation movement of the waist with the maximum range. The principle of waist motion measurement is shown in Figure 1.

After the post-processing in Cortex, the data of waist twisting have variability, which is similar to the data of human gait. After segmenting the original data and fitting them with Fourier functions, the rationality of the characteristic parameters such as the number of collected points, the fitting residuals and the deviations of key fitting parameters are judged. The unreasonable data are eliminated through various rationality judgments, and the key parameters are averaged to obtain the final fitting results. The fitting functions in X and Y directions can be expressed as:where \({a}_{x}\) and \({a}_{y}\) are the coordinates of the center point of the fitting trajectory, respectively. \({a}_{x}^{^{\prime}}\) and \({a}_{y}^{^{\prime}}\) are the amplitudes in X and Y directions, respectively. ω is the fitting frequency.

Take the data collected from Volunteer 1 as an example. Due to the different number of points collected in each waist twisting cycle, the key fitting parameters are obtained by fitting the data segment of each waist twisting cycle separately. After distinguishing the number of data points of each data segment, the fitting results of key parameters in X and Y directions are shown in Tables 1 and 2, respectively. According to normal distribution guidelines, the 3σ values of key parameters are obtained after removing the maximum and minimum values. In Table 1, the data in the 10^th segment is judged as an abnormal segment, and the fitting data are averaged after removing it. Finally, the accurate fitting result of the waist trajectory is obtained.

Figure 2 shows the comparison of the fitting results of the waist motion in the horizontal plane before and after the rationality judgement. It can be seen from Figure 2 that the results obtained after removing the abnormal data are closer to the real situation. By judging the rationality of the data, the problems of different amounts of data points and fitting frequency in each cycle are solved, and the drift of the center point is fully considered to a certain extent.

Based on this, the fitting results of the waist motion trajectory in the horizontal plane are obtained. The center point of the human waist in a standing state, and the center point of the human waist at the front, back, left and right endpoints in the waist twisting are selected as feature points, which are noted as A₁(0,0,0), A₂(\({a}_{x}^{^{\prime}}\),0,\({h}_{1}\)), A₃(0,\({a}_{y}^{^{\prime}}\),\({h}_{2}\)), A₄(\({-a}_{x}^{^{\prime}}\),0,\({h}_{1}\)) and A₅(0,\({-a}_{y}^{^{\prime}}\),\({h}_{2}\)), respectively.

The feature points obtained in Section 2 are represented in Figure 3. The projection of the waist motion path of seven feature points with determined coordinates in the horizontal plane is composed of two line segments and an ellipse. Points A₁ and A₇ are the start and end points of the trajectory, respectively. Points A₁ and A₇, A₂ and A₆ are coincident, respectively. Points A₂₍₆₎, A₃, A₄ and A₅ are the endpoints of the ellipse. The set of all passing points is symmetric about A₁A₂, and the sequence of each point is A₁(0,0,0), A₂(\({a}_{x}^{^{\prime}}\),0,\({h}_{1}\)), A₃(0,\({a}_{y}^{^{\prime}}\),\({h}_{2}\)), A₄(\({-a}_{x}^{^{\prime}}\),0,\({h}_{1}\)), A₅(0,\({-a}_{y}^{^{\prime}}\),\({h}_{2}\)), A₆(\({a}_{x}^{^{\prime}}\),0,\({h}_{1}\)), A₇(0,0,0). \({a}_{x}^{^{\prime}}\) and \({a}_{y}^{^{\prime}}\) denote the endpoint values on the short axis and long axis of the ellipse, respectively. \({h}_{1}\) and \({h}_{2}\) denote the Z-axis coordinates at the corresponding endpoints, respectively. The fitting data of Volunteer 2 with acceptable dispersion and relatively large amplitude of waist twisting are selected as the feature points in trajectory planning. At this time, the values of \({a}_{x}^{^{\prime}}\) and \({a}_{y}^{^{\prime}}\) are 78 mm and 102.5 mm, respectively. And the length H of human lower limbs is 1100 mm. According to the selected feature points, the motion path of the center of the human waist is shown in Figure 3.

The trajectory of the center of human waist can be expressed as:where \({a}_{x}^{^{\prime}}\) and \({a}_{y}^{^{\prime}}\) are the endpoint values on the short axis and long axis of the ellipse, respectively. ω denotes the frequency. \({t}_{1}\) denotes the time from A₁ to A₂. The time scale factor is defined as \({k}_{t}={4t}_{1}/{t}_{2}\).