Robotic investigation on effect of stretch reflex and crossed inhibitory response on bipedal hopping

To maintain balance during dynamic locomotion, the effects of proprioceptive sensory feedback control (e.g. reflexive control) should not be ignored because of its simple sensation and fast reaction time. Scientists have identified the pathways of reflexes; however, it is difficult to investigate their effects during locomotion because locomotion is controlled by a complex neural system and current technology does not allow us to change the control pathways in living humans. To understand these effects, we construct a musculoskeletal bipedal robot, which has similar body structure and dynamics to those of a human. By conducting experiments on this robot, we investigate the effects of reflexes (stretch reflex and crossed inhibitory response) on posture during hopping, a simple and representative bouncing gait with complex dynamics. Through over 300 hopping trials, we confirm that both the stretch reflex and crossed response can contribute to reducing the lateral inclination during hopping. These reflexive pathways do not use any prior knowledge of the dynamic information of the body such as its inclination. Beyond improving the understanding of the human neural system, this study provides roboticists with biomimetic ideas for robot locomotion control.

has been investigated in human walking [23], more studies are needed to confirm that the change in dynamics caused by these pathways contribute to the balance in locomotion.
Since both stretch reflex and crossed inhibitory response modify the activities of muscles in the bipedal legs, it can be speculated that they influence the posture in the frontal plane during locomotion. For example, when a human lands with lateral inclination in hopping, the soleus muscle in the first touchdown leg (leaning side) is stretched stronger and generates a larger afferent feedback than that of the soleus muscle in the second touchdown leg. Since larger afferent feedback induces a stronger crossed inhibitory effect [18], the muscular activity of the second touchdown leg should be inhibited stronger by the crossed response compared to that of the first touchdown leg. This difference of muscular activity may cause an incorporation of ground reaction force (GRF) between the two legs, thus help the body reduce the lateral inclination. While, because dynamic locomotion is affected by the neural networks, musculoskeleton, and environment, it is very difficult to make a rational explanation with the absence of experiment.
In this study, we implement a robotic constructive experiment since it is difficult to fully understand the effects of these reflexes to the dynamic locomotion by conventional approaches, such as experiments on human and simulation.
Although experiments on humans can identify the neural pathways, it is difficult for them to clarify the effects since they cannot remove the effects of other neural and cognitive processes in living animals [6] [24]. A simulation fall short of this target because the body dynamics including touchdown dynamics are very complicated and difficult to be well modeled in a visual environment [6]. In recent years, performing experiments on bio-inspired robots has been demonstrated to be a powerful approach for understanding human/animal locomotion, and is gathering increased attention [6] [25] [26] [27]. Therefore, we built a musculoskeletal robot that has body dynamics similar to a human; especially, our robot takes the precise anatomical details into account together with the actuation patterns derived from electromyography (EMG) data.
The rest of the paper is organized as follows. First, we introduce the constructive experiment, including the used hardware, the implementation of the reflexive control by artificial muscles, and the experiment protocol to show the effectiveness of the reflexes. With 382 hopping trials, we demonstrate that stretch reflex can help reducing the lateral inclination, and the combination of stretch reflex and crossed response can contribute to the reduction of the lateral inclination even further.
II. METHODS Fig. 1 shows the musculoskeletal bipedal robot used for the experiment. This robot is built to mimic the human neural networks, muscles, and skeleton. It is designed based on the following four ideas: • Each robot leg has nine representative muscles that imitate the hopping action of a human [28] [29] [30] [31].
Soft and elastic pneumatic artificial muscles (PAMs) are used as the actuators of the robot. A PAM contracts when compressed air is supplied, and relaxes when the air inside the muscle is exhausted. The tensile force of a PAM is a function of the deformation and inner air pressure [32].
• The hopping control ( Fig. 2   Crossing the spinal cord, the afferent feedback ( Fig. 3(a) A1) inhibits the soleus muscle activity of the contralateral leg ( Fig. 3(a) A3) [36] [20]. This is the crossed inhibitory response in human. When a human lands with lateral inclination, the soleus muscle of the first touchdown leg (the leaning side) is stretched stronger and generates a larger afferent feedback compared to that of the soleus muscle in the second touchdown leg. Because larger afferent feedback induces a stronger inhibitory effect [18], the first touchdown generates a stronger crossed inhibitory response to the second touchdown leg compared to that generated by the second touchdown to the first (shown in Fig. 3(a)). Our robot is designed to mimic this cross inhibitory response behaviour qualitatively: the first touchdown signal inhibits the air supply of the contralateral soleus muscle (Fig. 3(b) B1 to B3), while the second touchdown signal of the contralateral leg does not generate crossed inhibitory response.
We tested three cases of reflexive control, representing different combinations of stretch reflex and crossed inhibitory response (shown in Table I). The control of air supply for each case is shown in Fig. 2(c).  The lateral inclination of landing was constrained within (−6 • , 6 • ). The reason behind this is that if a human lands with a large inclination, it is necessary to change the locomotion pattern to maintain the posture, which needs to include other controls such as the control from brain [37].

III. RESULTS
To get an insight into the effects of the reflexes, in soleus muscle and the lateral inclination is barely affected.
In the SR case, both the soleus muscles are activated. Due to the inclination, a greater P sol (which indicates a greater ground reaction force) is generated by the first touchdown (left) leg and a shifting trend of θ is induced. In the SR-CIR case, due to the crossed inhibitory response, the activity of the soleus muscle in the second touchdown leg is inhibited and a greater shift of θ is achieved during the stance phase. Compared to the NONE case, SR shows a smaller slope and a significant difference (P < 0.01, two-tailed unpaired t-test after Bonferroni correction). Moreover, SR-CIR exhibits a smaller slope and is significantly different from the SR case (P < 0.001, two-tailed unpaired t-test after Bonferroni correction).
This shows that both the stretch reflex and crossed inhibitory response contribute in decreasing the lateral inclination.  In our investigation, although we demonstrated that both the stretch reflex and crossed inhibitory response contribute to the reduction of lateral inclination, even the best scenario (SR-CIR) did not show posture recovery after lift-off. This is reasonable. First, human locomotion is controlled by numerous muscles. Stretch reflex occurs not only in the soleus muscles but also in other muscles such as vastus lateralis [38] and me- inclination, the applied control is the same (the air supply for stretch reflex is equal between the two legs). Landing with an inclination causes different amounts of muscle stretch between the two legs ( Fig. 4(a) and (b)). In the SR case, the activated soleus muscle in the leg with stronger stretch (leaning side) generates a greater reaction force (GRF) than the corresponding muscle in the contralateral leg with weaker stretching (Fig. 4(b)). Additionally, the muscle with stronger stretching restores and returns more energy during the stance phase. In contrast, in the NONE case ( Fig. 4(a)), both the relaxing soleus muscles react only slightly to the stretch, and therefore the posture is not significantly influenced.  recovery (Fig. 4(c)). Moreover, our result corresponds to the recent investigation of crossed response during walking. By comparing the subjects with and without short latency crossed response, Gervasio et al. [23] determined that the short latency crossed response can influence the lateral inclination of the body, and suggested that crossed response contributes to the dynamic walking stability.
Considering the similarity between hopping and standing (e.g. bipedal support stance phase), the comparison between the SR case and NONE case also provides an insight into understanding the observed phenomenon in the experiments of human standing. For example, it was widely observed (also from common sense) that when a human is in unstable/threatened situations (e.g., changes in body orientation [47], standing on a high platform [48], and possibility of support surface change [49] [50]), the muscles tend to get facilitated stronger compared to that in safe situations. Scientists speculated that this phenomenon may contribute to posture stability [48]. In our research, we demonstrated that equally facilitating the muscles in both legs by stretch reflex can help in posture balance (SR case VS. NONE case in Fig. 6) and supported this speculation. Similar to that in other robotic studies trying to mimic biological behaviour, our approach has certain limitations.
The developed artificial system cannot perfectly replicate the biological body. For example, some properties of biological muscles, such as force-length relationship [42], which can improve the hopping stability, are absent in PAMs [52]. For the stretch reflex and crossed inhibitory response, the magnitude is related to the afferent input in humans [18], whereas its replication on the robot is constant. Furthermore, we used FSRs to detect the start of muscle stretching. Actually, in biological muscles, the stretch is sensed by muscle spindles.
Although we are developing artificial muscle spindles to mimic this natural phenomenon [53], the present setting with FSRs would be sufficient to functionally reproduce the stretch reflex and crossed inhibitory response. These issues still need to be solved in future.
Author's Contribution

Competing Interests
We declare that we have no competing interests.

Funding
This work was supported by JSPS KAKENHI grant number 16J05748, 17H05908, and 23220004.

Acknowledgment
The PAM is considered as one of the most efficient and widely used artificial muscles [32]. With properties such as elasticity, softness, morphology, and high power-weight ratio, we chose PAMs as the robot actuators (samples of PAM are shown in   where F is the force output, D 0 is the diameter without air supply, P air is the internal air pressure, and θ represents the angle of the braid (a parameter to describe the deformation).

APPENDIX B MUSCULOSKELETON
Based on the observed muscle activity in human hopping, to power the robot achieving jumping, we equipped nine representative muscles in each leg. Those muscles are significantly activated in human hopping. Six of these muscles are monoarticular muscles and three are biarticular muscles.
Two soleus muscles are installed in parallel in each leg. One is used as actuator and the other is used to replicate stretch reflex. The musculoskeletal structure is shown in Fig. 1.

APPENDIX C JUMPING CONTROL
The on-off air valves (VQZ1000 series, SMC Corporation) were used to control the air flow of artificial muscle. The monoarticular muscles were determined to contribute to power generation and the biarticular muscles contribute to the coordination of joints [54] [55]. Similar findings in vertical jumping can be found in [29] [56]. Consequently, in the motion control, we only activated the monoarticular muscles and kept the air in the biarticular muscles constant. In human hopping, as the gastrocnemius muscle is stretched to nearly its longest length in bottom position [9], we detected the bottom position by measuring the peak of air pressure in a gastrocnemius muscle (P gas ) (described by the following equation filter to obtain the lateral inclination.
The complementary filter estimated the lateral inclination by using the one-axis data from gyroscope and two-axis data from the accelerometer. First, the accelerometer information of both Y and Z axes were used to find the angular projection in the frontal plane: θ a(x,n) = arctan( y z ), where y and z represent the acceleration information in Y and Z axes respectively. θ (x,n) is the lateral inclination (about X axis) calculated by the accelerometer.
The accelerometer shows fast reaction and large noises, whereas the gyroscope has a more stable output but with larger delay. We estimated the body lateral inclination by combining the calculation of accelerometer and gyroscope. The estimated lateral inclination is presented as follows: θ e(x,n) = θ a(x,n) + wθ g(x,n) 1 + w , where w is the filter weight set as 90 in this experiment and θ g(x,n) is the lateral inclination output of the gyroscope.
Considering that the accelerometer registers angular velocity, the gyroscope used a previous angular estimation to update itself: θ g(x,n) = θ e(x,n−1) +θ g(x,n) T where T is the sampling duration.