Since the upper limb dysfunctions after stroke seriously affect daily lives, it is essential for patients to restore the affected motor functions through rehabilitation training. Post-stroke reaching movements is affected by gravity weight of upper limb due to the weakness of those anti-gravity muscles (Beer et al., 2007). Position control was adopted in traditional robots (Lahouar et al., 2009; Yuan et al., 2014) and rehabilitation robots (Lum et al., 2002; Staubli et al., 2009), to follow predetermined trajectories. Although, position control in rehabilitation robots could counteract the effect of gravity weight of upper limb, it focused on control accuracy and ignores patients' voluntary participation in task execution, and its effectiveness in rehabilitation therapy needed further improvement. For patients who suffer from muscle weakness, gravity support showed promising results in minimizing the gravity-induced interference for tasks execution (van Elk et al., 2005; Cheng et al., 2015; Runnalls et al., 2015).

Gravity compensation can be provided by support devices (Herder et al., 2006; Kloosterman et al., 2010) or robotics (Kahn et al., 2006; Ball et al., 2007; Ladenheim et al., 2013), and can be generally grouped into three categories. Firstly, fixed or manually adjusted compensation were commonly used to counteract the gravity weight of upper limb (Nef et al., 2007; Stopforth, 2013; Lenzo et al., 2015). Similarly, a fixed external vertical force was applied to an upper limb robot by a motorized vertical cabling system for gravity compensation (Ball et al., 2007). Secondly, passive compensations by flexible force from elastic materials were chosen (De Luca et al., 2005; Stienen et al., 2009). As an assistive arm exoskeleton, T-WREX provided gravity compensation from the elastic bands whose number could be adjusted at different arm support levels (Housman et al., 2009). Arm orthosises with springs was designed to passively compensate arm weight, and could help patients with little moving ability to reach and grasp (Herder et al., 2006; Kramer et al., 2007). Freebal, a device with gravity compensation at different levels from cables connected to springs, could facilitate upper limb movements tracking in the horizontal and vertical planes (Prange et al., 2009; Kloosterman et al., 2010; Coscia et al., 2014). Thirdly, position-varying compensations can be provided according to human physical characteristics, since gravity torque of upper limb is highly coupled with the dynamics of the limbs and dependent on the postures and positions of moving limbs. Hsu et al. proposed an active control strategy to estimate the subject's movement intention and the control strategy included a gravity compensation term modified by the upper limb dynamics (Hsu et al., 2012). Cheng et al. developed a two degrees of freedom (2-DOF) compliant beam which could compensate the torques on each joint based on the dynamic of the upper limb (Cheng et al., 2015). A torque-angle model containing a gravity compensation term was proposed by Lin et al. to evaluate motion quality of adhesive capsulitis patients (Lin et al., 2014).

Since the gravity torque is highly dependent on positions of upper and fore arm during movements, fixed or varying elastic compensation strategies did not consider the position-coupling effect. Although, Hsu et al. and Li et al. included compensation strategies according to human physical characteristics, both their strategies were combined with other control terms (Hsu et al., 2012; Li et al., 2015) which might affect voluntary participation. Gravity compensation should provide suitable assistance to subjects without affecting voluntary participation, but few previous studies about compensation strategy considered both varying position of upper limb and voluntary participation. Meanwhile, how varying position affects movement performance and muscle activations is rarely reported.

The objective of this study is to develop a position-varying gravity compensation strategy for a cable-based rehabilitation robot. A gravity torque estimation model according to position feedback is proposed for estimating real-time upper limb gravity torque. Then, the performance of this strategy is compared with the other two kinds of gravity compensation strategies (i.e., without compensation and with fixed compensation) during four different directions of man-machine cooperation movements tracking. Root mean square error (RMSE) between target and actual moving trajectories, normalized jerk score (NJS), mean velocity ratio (MVR) of main motion direction, and the mean activation of six muscles are used for assessing different compensation strategies with a cable-based rehabilitation robot.

Figures 3A–C displayed RMSE (Figure 3A), NJS (Figure 3B), and MVR (Figure 3C) during movements tracking with different gravity compensation strategies. The results of ANOVA tests were shown in Table 1. As shown in Table 1, both compensation strategy and movement direction showed notable influences on RMSE (P < 0.05), NJS (P < 0.05), and MVR (P < 0.05). No significant interaction between compensation strategy and movement direction was found. The results showed that there were significant effects of compensation strategies in RMSE and NJS values represented by the following order: without compensation > fixed compensation > position-varying compensation, and MVR values represented by the following order: without compensation < fixed compensation < position-varying compensation. According to the post-hoc analysis, RMSE during upward and forward movements were remarkably higher than those during the leftward and rightward movements while MVR during upward and forward movements were significantly smaller than those during the leftward and rightward movements. Additionally, there was a significant decrease in NJS during upward movements compared with those during rightward movements. Based on paired t-test, RMSE of position-varying compensation strategy reduced significantly in leftward and rightward movements when comparing with those of without and fixed compensation strategy. In upward and forward movements, significant difference between the RMSE values of the position-varying and fixed compensation strategies were found. As for NJS, the significant difference between the position-varying and without compensation strategies during upward and forward movements and the significant difference between the position-varying and without compensation strategies during upward movement were found. All the MVR values with fixed and with position-varying gravity compensation were larger than those without gravity compensation. Comparisons of MVR between each two of three gravity compensation strategies showed significant difference in three directions: upward, leftward, and rightward. The actual trajectories in four movements from a same subject were plotted in Figure 3D.

Figure 4 represented EMG envelope of the six muscles for one subject during the movements tracking with three different compensation strategies. The results indicated that when the subject moved upward, leftward, and rightward with gravity compensation, BIC, DA, DM, and TRA were less activated while he moved rightward, BIC and DA were less activated. Two-way ANOVA showed that effect of compensation strategy on mean muscle activation of BIC, TRI, DA, DM, and TRA (P < 0.05) together with effect of direction on mean muscle activation of DA, DM, and TRA were significant (P < 0.05). No significant interaction between compensation strategy and movement direction was found. In Figure 5, mean muscle activation of per muscle during four direction movements with different gravity compensation strategies were displayed. Compared with movements without compensation, the mean activation of some muscles during movements with position-varying compensation showed significant reductions [i.e., BIC and DA in all four directions, the mean activation of DM and TRA in three directions (forward, leftward, and rightward), and the mean activation of TRI in both upward and rightward]. The results revealed that the activation of BIC, TRI, DA, and DM with position-varying gravity compensation showed a significant decrease compared with fixed compensation during the upward movements.

The purpose of this study was to compare three different gravity compensation strategies by a cable-based robotic system. Kinematics parameters in terms of RMSE, NJS, and MVR together with mean muscle activations were applied to evaluate their movement performance. RMSE can reflect the general tracking accuracy, and is determined by sensory perception, motor planning and execution (Seppänen et al., 2013). The lower RMSE values with position-varying gravity compensation reflected improved tracking accuracy, which was in agreement with previous studies (Grimm et al., 2016). NJS reflected movement smoothness and was generally utilized to evaluate the arm control abilities (Adamovich et al., 2009). The significant decrease in NJS with compensation than without compensation were also reported by Coscia et al. who found significant difference in normalized jerk between without and with gravity compensation during arm reaching movements (Coscia et al., 2014). MVR is utilized to quantify the relative velocity deviation in desired direction during movements tracking. A similar parameter, normalized angular velocity ratio, was proposed by Kim et al. for assessing locomotion precision (Kim et al., 2014). The higher MVR values with position-varying gravity compensation indicated that subjects could more voluntarily participate in the desired movements. The effects of direction on movement kinematics were significant which was in accordance with previous studies in sagittal (Papaxanthis et al., 1998), frontal (d'Avella et al., 2008), or horizontal plane (Beer et al., 2004). Both RMSE and MVR could describe movement accuracy from different points of view, and higher RMSE during upward and forward movements were corresponding to lower MVR. There explanation of the result might be that, the variation of gravity torques during upward and forward movement might be larger.

There were significant reductions in main contributed muscle activations with position-varying and with fixed gravity compensation when compared with without compensation. Previous studies also found that BIC, DA, and TRA were the mainly contributed muscles for gravity support of upper limb, and the activations of these muscles also decreased significantly during movements in horizontal plane (Sabatini, 2002; Prange et al., 2009) and frontal plane (Kloosterman et al., 2010; Coscia et al., 2014). In addition, McCrea et al. proposed that DM was recruited if the primary anti-gravity muscles were not capable during upper limb movements (McCrea et al., 2005). The findings of this study were in accordance with the above-mentioned studies. Although, upper limb muscles activations were dependent on direction (Hughes et al., 2009), activations of DP and TRI were not affected by direction in this study. It might be explained by that they were not the main contributed muscles indicated by in low activations in the four directions. As reported, subjects could maintain satisfy dynamic criteria during movements such as optimization of motor command (Nakano et al., 1999) or energy expenditure (Soechting et al., 1995) by appropriately activating arm muscles. The reduction of the mean muscle activation due to gravity compensation indicated that subjects could put more focus on target-directed movements, and result in a larger range of motion or more repetitions of movements. Previous studies also reported subjects had larger range of motion on the horizontal panel with gravity compensation (Housman et al., 2009; Wang and Dounskaia, 2012). Furthermore, muscle activation is related to muscle forces(Lloyd and Besier, 2003), therefore, lower activation of muscles might reflect the robot is able to share the gravity loading, and muscle forces mainly focus on desired movement execution.

This study found that position-varying gravity compensation provided by the cable-based rehabilitation robot could improve man-machine cooperation movements in 3D working space in terms of RMSE, NJS, and MVR, which was the first explorative investigation on the position-varying gravity compensation to our knowledge. Moreover, since the position-varying gravity compensation strategy could reduce activations of anti-gravity muscles, it could assist patients with muscle weakness to perform rehabilitation training in clinic. The advantages of the position-varying compensation strategy are located on two aspects: firstly, the assistance is provided to counteract the effect of gravity; secondly, the assistance does not let the training in the passive way, and voluntary residual motor efforts can be focused on target-directed task. The reorganization in brains of subjects after stroke can be facilitated by active rehabilitation training (Cauraugh et al., 2000). In the future, more parameters should be adopted to clarify performance of the position-varying gravity compensation, and patients should be employed to explore the clinical effectiveness.

The present study firstly explored the effect of position-varying gravity compensation strategy provided by a cable-based robot on kinematics and muscle activations in comparison with the other two gravity compensation strategies. The improvement in kinematics and less activated anti-gravity muscles with the position-varying gravity compensation indicated its potential in robot-aided rehabilitation therapy. More studies across pathologies with gender-matched subjects are needed to validate whether training with position-varying gravity compensation is clinically feasible and effective.

YH and RS conceived and designed the study. YH and QY performed the experiments. YH and QY wrote the paper. RS reviewed and edited the manuscript. YH and QY contributed to the work equally and should be regarded as co-first authors. YC made a contribution to experiments. All authors had read and approved the manuscript.

The project was supported by the National Natural Science foundation of China (Grant No. 61273359 and 91520201), the Guangdong Science and Technology Planning Project (Grant No. 2014B090901056 and 2015B020214003) and the Guangzhou Research Collaborative Innovation Projects (Grant No. 201604020108).