“RobOstrich” Manipulator: A Novel Mechanical Design and Control Based on the Anatomy and Behavior of an Ostrich Neck

Flexible manipulators have high degrees of freedom and deformability, enabling dexterous movements and allowing for unexpected contacts with the environment. Underactuated tendon-drive mechanisms are the most widely adopted because of their simplicity and effectiveness. However, they suffer from difficulty in modeling and in achieving dexterity and structural stability. In this letter, we focus on ostriches, which can dexterously and swiftly move their flexible necks. We carried out a detailed dissection of ostrich necks and identified a specific musculo-tendon-skeletal structure. Based on the findings related to the structure, we came up with a novel mechanical design and control method manifested as a “RobOstrich” manipulator. Our actual robot experiments confirm that it exhibits similar movement patterns as an ostrich neck. It is also flexible yet structurally stable, enabling dexterous reaching movements. This work also contributes to biology by providing constructive understanding of the functionality of the morphology of an ostrich neck.

manipulators have high degrees of freedom (high-DOFs) and deformability, similar to soft manipulators [2]. High-DOFs allows the manipulator to move dexterously. In this context, we consider dexterity as being the variation of different postures possible when the tip of the manipulator reaches the same point [3]. This variation allows the manipulator to perform subtasks [4]. The deformability is the property of continuous deformation in response to external forces, which allows for an interaction with environments safely and easily [2].

A. Flexible Manipulator and Its Drive System
For a manipulator to be flexible (deformable and high-DOFs), an underactuated driven system using tendons that penetrate the entire elastic body (underactuated tendon-driven system) has been proposed [5]. In this method, the actuator can be placed at the base of the manipulator, and the rotation angle at the middle part of the manipulator is determined by elasticity ( Fig. 1(a), blue line). These properties simplify and reduce the weight of the manipulator [7].
However, underactuated tendon-driven flexible manipulators have three main disadvantages. The first is difficulty in modeling. In tendon-driven system, wire elongation [8] and friction [9] in the wire path make modeling difficult and these complicate model-based control. The second disadvantage is their low dexterity of movement. Tendons that are placed to penetrate the entire elastic body make the manipulator's movement onedimensional, which makes it difficult to realize the subtasks during reaching [4], [10]. In contrast, an architecture of dividing the drive system into multiple sections serially and driving them independently has been proposed Fig. 1(b). However, this goes against the advantages of the underactuated driven system, which simplifies the mechanism by reducing the number of drive systems [10]. The third is their low structural stability. When a flexible structure is lifted and inverted against gravity, an antagonistic drive is required, but flexible and long materials relative to their diameter will buckle, causing large localized deformations. This results in large modeling errors and reduces the reachable distance of the tip. This causes difficulty in realizing continuum manipulators on the metric order [11].

B. Bio-Inspired Flexible Manipulator
Biology has been a source of inspiration for robotics researchers who want to design and control flexible manipulators. The animal trunk has vertebrae connected by smooth cartilage and is tendon-driven by multiple developed long muscles [12]. Therefore, the trunk can be regarded as a structure similar to a flexible manipulator that utilizes an underactuated tendon-driven system. Consequently, a number of manipulators have been proposed that imitate the trunk of an animal [13], [14]. Among animal trunks, the avian neck has approximately 20 cervical vertebrae, compared with seven in mammals, and each cervical vertebra bends in two directions, making it exhibit extremely high DOFs [15]. The ostrich, the largest species of bird, uses its one-meter-long, flexible neck dexterously as a manipulator. It is expected that focusing on the largest birds minimizes the impact of scale differences between animals and robots. Thus, the biological insights of an ostrich neck can be a useful guideline for designing flexible manipulators. Therefore, we developed a manipulator that incorporates the morphology of an ostrich's muscle-tendon arrangement and skeletal structure [16]. The realized manipulator was able to lift the flexible structure against gravity because of the antagonism of the ventral (abdominal side) and dorsal (back side) long muscles. However, this antagonism made the manipulator's movement one-dimensional, so dexterous reaching with high DOFs could not be achieved. In addition, its low structural stability was not resolved because the antagonistic balance strongly depends on the initial state of the manipulator. To manipulate flexible structures with structural stability and dexterity, researchers should clarify the control laws used in the coordination of antagonistic muscles and the role of morphology in ostrich neck movement.
Therefore, the objective of this study is to develop an ostrichinspired flexible manipulator capable of reaching movements with both structural stability and dexterity. This letter is organized as follows: Chapter II describes in detail ostrich neck movement patterns and their related morphology. In chapter III, we propose a kinematic model for ostrich neck movement and our assumption regarding the function of the morphology. We also detail the RobOstrich manipulator (shortened form of robotic ostrich manipulator) that was built based on this assumption. Chapter IV describes the basic verification of the behavior of the RobOstrich manipulator, a demonstration of dexterous movement, and the role of the implemented morphology on structural stability and dexterity. This letter has three contributions: r We proposed a novel wire arrangement and control method, that performs the same movement as the ostrich's neck by integrating our findings from the dissection with previous studies on bird's necks.
r We formulated the ostrich neck movement pattern as a novel kinematic model for control, and discussed the method of reaching by using it for feedback. r Systematic experiments with the manipulator showed that morphology, such as joint angle limit and muscle-tendon arrangement, provides dexterity and structural stability to flexible manipulators. These results are suggestive for biology because they indicate that actual birds may also use the proposed mechanism and control laws.

II. CERVICAL KINEMATICS AND ANATOMY
The neck movements of birds are extremely variable, but because of the symmetry of their neck structure, feeding behavior in sagittal plane has been the focus of widespread research. These studies have revealed that a certain pattern exists in the rotational movement of each joint during feeding behavior. These movement patterns and morphology are closely related to each other [17], [18], [19]. Neck movement patterns and morphology show the similarities among terrestrial birds [19]. In the following sections, we discuss ostrich neck movement, here referring to previous studies on chickens, which are terrestrial birds like ostriches. Note that we purchased carcasses of the neck from ostrich ranch and dissected it in this study.

A. Cervical Movement Pattern
Previous studies have led to several rules for neck movements during the feeding behavior [15]. In a repetitive movement, such as feeding, 18 cervical vertebrae are not controlled independently, but instead, they are coupled with each other based on certain rules. The rules allow the entire neck shape to be described by a lower dimensional two-link model [15]. The first rule is to maximize the displacement of the head with respect to the total changes in the joint angles for energy-efficient movements. As a result, bending deformations are concentrated in two areas: near the base and middle of the neck. The pecking behavior observed during feeding is considered a two-link-like behavior that follows this rule and is called the lever pattern Fig. 2(a). The second rule is to reduce the torque applied to the base joint when the movement pattern according to the first rule results in excessive torque. The movement pattern of raising the head while keeping it level with the ground follows this law and is called a rolling pattern. The rolling pattern can be interpreted as a continuous change in bending position and link length in a two-link model Fig. 2(b). Ground-feeding birds move their heads up and down in a rolling pattern and peck at objects in the lever pattern [19].

B. Muscle-Tendon Arrangement of an Ostrich Neck
As Fig. 3(a), and (b) shows, an ostrich neck is a complicated antagonistic tendon-driven system composed of numerous muscles. However, the kinds of developed long muscles that contribute significantly to the overall movement are limited. Hence, the focus is mainly on musculus longus colli dorsalis (m.long.col.dors.) and musculus flexor colli lateralis/medialis (m.flex.col.lat./med.) in terms of mass percentages [18].
In addition, the origin and insertion of these developed muscles and the cross-sectional views at each cervical vertebra were clarified by the dissection. By taking these two findings into consideration, we can determine the region (i.e., the point of action) where the contractile force of the developed long muscle acts. In the dorsal side, m.long.col.dors. is divided into three groups (pars cranialis (cr.) Fig. 3(c), pars caudalis (ca.) Fig. 3(c), and pars profunda (pr.) Fig. 3(d)) according to their attachment site [18]. As can be seen from Fig. 3(c), in m.long.col.dors.cr. and m.long.col.dors.ca. are concentrated on the caudal side and the cranial side, is driven by long tendons. Focusing on the caudal side of the dorsal side (red dashed line), the cross-sectional area of the dorsal muscle increases significantly from C14. Not all of these muscles are m.long.col.dors.pr., but focusing on Fig. 3(f), these muscles are intensively attached to the C14 joint. This suggest that the dorsal muscles may pull C14, the point of action, strongly against the base. On the ventral side, focusing on the cross-sectional views near the middle of the neck (black dashed line), the muscles are particularly developed near the C6 to C10 joints. Taking this and the origin and insertion positions of the m.flex.col.lat./med. into account, it is possible that the forces acting on each cervical vertebrae cause the neck to flex strongly to the ventral side.

C. Skeleton and Articulation of an Ostrich Neck
Skeleton structures reflect the movement pattern of the neck [17]. Therefore, as a skeletal structure, the length and joint range of motion of the cervical vertebrae will be detailed. The total length of the ostrich neck is approximately one meter. The length of the cervical vertebrae tends to shorten toward the head. In addition, the saddle-shaped surfaces at the cranial (head side) and caudal (tail side) ends of each cervical vertebra allow for flexion to the dorsoventral side and lateral side, as shown in Fig.  4(a), and (b). These surface structures and ligaments limit the range of motion, which varies from joint to joint. The length of each joint (interaxial distance) and the dorsoventral range of motion are shown in Fig. 4(d) [17].

III. DESIGN OF THE ROBOSTRICH MANIPULATOR
In this chapter, we first propose a novel kinematic model that formulates the movement of an ostrich's neck, and assume that the joint angle limit couples the joints to generate this global property. Next, we propose a novel mechanical system with a wire arrangement that mimics the developed long muscles revealed by our dissection. Furthermore, we made assumptions about the control law of the muscles based on previous studies on the motor pattern of bird's neck. In accordance with this assumption, we proposed a control law for the mechanism to realize the kinematics of an ostrich neck. The novelties of this mechanism to conventional flexible manipulators are to actively utilize the joint angle limit, and to have long muscles on the dorsal side. These merits are described in Sections IV-E and IV-F, respectively.

A. Kinematic Model of an Ostrich Neck
As mentioned in Section II-A, one joint does not move locally, but multiple joints work together to form the shape of the entire neck in the neck's motion. The shape can be modeled as a curve that bends at two points and changes one of the bending positions. Here, the shape of the curve at the bending area is approximated as a circular arc [6]. Therefore, the homogeneous transformation matrix can be determined as follows: The parameters of the transformation matrix are listed in the table in Fig. 5 Consequently, by finding B C T and C T T in the same Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply. way, the tip position can be written as: In this model, the joint angle limit is assumed to prevent excessive deformations and create coupling between joints (detailed in Section IV-F).

B. Muscle-Tendon Arrangement of the RobOstrich Manipulator
In Section II-B, we clarified the muscle arrangement and the regions where the muscle force acts, as shown in Fig. 6(a). Fig. 6(b) shows the motor and wire arrangements of the Ro-bOstrich manipulator, which was implemented based on these findings. A high-strength polyethylene fiber wire (Dyneema ULTRA2 No.15) was used on the dorsal side to mimic the tendons of an ostrich neck. In Fig. 6, wire 1 was fixed to the dorsal side of C6 to mimic the m.long.col.dors.ca. Also, as shown in Fig. 3(f) and (g), the dorsal m.long.col.dors.pr is more considerably developed on the caudal side than C14. Correspondingly, wire 2 was fixed to the dorsal side of C14 and placed in the same manner as wire 1. Wires 1 and 2 were pulled by two back drivable motors (T-motor AK80-6) located at the base. On the ventral side, ostriches have a mesh-like structure: m.flex.col.lat./med. We consider its functionality of bending vertebrae to the ventral side sequentially (detailed in III-C). It is this functionality that should be transferred to the robot, not appearance of the morphology [20]. Therefore, a group of tendon drive mechanisms was placed between the ventral side of joints C6 and C9 corresponding m.flex.col.lat./med. In the tendon drive mechanism, the wires were independently connected to the pulleys via outer cables and pulled by a servo motor (Dynamixel XM540-W150-R).

C. Motor Pattern
To actuate the manipulator following the kinematic model of Section III-A, we have hypothesized the control laws of the ventral and dorsal muscles based on biological knowledge. Of the three types of long muscles developed in the dorsal side (m.long.col.dor cranialis, caudalis and profunda), cranialis was considered to contribute to head movement because the muscle is concentrated in the head, and we considered that caudalis and profunda contribute primarily to neck movement. Consequently, the cranial and caudal parts can be flexed dorsally by contracting these muscles. As a result, the lever pattern can be realized by controlling the dorsal muscles of these two parts Fig. 7(a).
Next, we discuss how the ventral muscles contribute to neck movement. In chickens the length of the dorsal long muscle hardly changes from its initial length during the rolling pattern [21]. In addition, not only the dorsal long muscle, but also the ventral muscle increases its electromyography potential [22]. In addition, as can be seen from the cross-sectional view of the ostrich neck shown in Fig. 3(g), the ventral muscles are developed at C6 to C12. Based on these findings, we assume that a rolling pattern is realized by sequentially pulling the ventral muscle, while keeping the length of the dorsal muscle constant Fig. 7(b). Fig. 8(a) shows the RobOstrich manipulator. This manipulator is the same size as an ostrich, 1 kg in mass (the ostrich's neck is approximately 3 kg in mass [18]). Each cervical vertebra was fabricated using 3D-printed nylon. Each cervical vertebra moved smoothly on bearings Fig. 8(b). The design parameters for each joint were the inter-axial distance and joint angle limit, as in the actual ostrich, according to Fig. 4(d). The joint angle limits were implemented with a nylon tie bands. A ceramic bushing was used on the dorsal side to reduce friction with the wire. In addition, five bundles of piano wire (d = 1.2 mm) were placed on the sides for gravity compensation to reduce the energy required for driving, here imitating of the intervertebral muscle [18] Fig. 8(c). Tension was applied to the dorsal side of the C18 to C11 joints by rubber bands to mimic ligaments Fig. 8(d). This was installed for safety during dynamic neck movements. The joint angles were measured by potentiometers (RDC503052 A) placed at each joint. For safety, the head and C1 joint, which weighed 170 g, were removed in subsequent experiments. Consequently, the tip of the C2 cervical vertebra became the tip of the RobOstrich manipulator. Therefore, the RobOstrich manipulator has 17 DOFs and 6 control inputs.

IV. EXPERIMENTS
This chapter first examines the movement patterns of the Ro-bOstrich manipulator, which was built based on ostrich anatomy. Second, we quantified the modeling error with the proposed kinematic model and discussed how to address these modeling errors through feedback using kinematic models. Third, the dexterous reaching task with the RobOstrich manipulator will be demonstrated. Finally, we show our experiment of a systematic comparative study to clarify the functionality of the implemented morphology.

A. Motor Pattern of the Manipulator
In this section, we show that the movement of the RobOstrich manipulator has the same characteristics as the neck movement shown in Section II-A. Fig. 9(a)-(b) show the shape of the actual RobOstrich manipulator when dorsal wire 1 (solid green line) and wire 2 (solid red line) have been pulled alternately from the initial posture (solid black line), respectively. This figure illustrates that the cervical vertebrae have multiple joints that are coupled without causing large local deformations. Furthermore, wire 1 contributed mainly to the movement of the cranial side, whereas wire 2 contributed mainly to the movement of the caudal side. In other words, the same movement on the sagittal plane as in the two-link system could be realized as in the lever pattern shown in Section II-A. The shape of the RobOstrich manipulator when the ventral mechanism was pulled is shown by the solid blue line in Fig. 9(c). Fig. 9(d) shows the shape when wire 1 was pulled by the same amount while the center x of the bending position is shifted caudally by the mechanism on the ventral side. The displacement of the tip increased in steps for the same amount of traction of wire 1 by the ventral mechanism. That is, the length of the links could change in the two-link system model.
Therefore, based on the assumption of the function of morphology in Section III-A and Section IV-A, the RobOstrich manipulator could realize movements with the same characteristics as the neck movements of the ostrich neck shown in Section II-A.

B. Reaching
In this section, the modeling error for the amount of wire pull is quantitatively evaluated to realize neck's tip reaching using the proposed model. The dashed lines in Fig. 9(a)-(c) show the posture predicted by calculating the change in each variable in the kinematics model based on the amount of wire pull. Comparing the solid and dashed lines shows that the head displacement in the actual posture was smaller than the predicted posture. The possible causes behind this include wire elongation, friction in the wire path, and the effects of gravity.
Despite the presence of such modeling errors, reaching was possible through human operation. Fig. 10 shows an experiment in which the target position and entire manipulator have been observed from the side and where the manipulator was operated manually for reaching. Assuming success when the tip of the manipulator overlapped the target position, multiple target points could be reached, as shown in Fig. 10. That is, if the difference between the manipulator's tip position and target position could be fed back and motor commands obtained based on the current posture, reaching would be possible without calculating the absolute tip position based on a model that precisely account for friction, gravity, etc.

C. Reaching Method Based on the Proposed Model
In this section, the discussion in Section IV-B is first formulated by the proposed model. First, the RobOstrich manipulator is approximated, and the Jacobian matrix at that orientation is computed. The Jacobian matrix is expressed as follows for the x-coordinate X Tip and y-coordinate Y Tip of the tip position O P Torg derived from (3): The Jacobian matrix satisfies the following equations: Thus, by calculating ΔX Tip and ΔY Tip for a given motor command (Δκ 1 , Δκ 2 , Δx) T and applying them to the following equations, the direction φ [deg] the tip travels in the next time step can be derived (evaluated in Section B): Conversely, if the difference (ΔX Tip , ΔY Tip ) T between the target position and tip position can be observed, the necessary motor command can be calculated using the following formula:

D. Dexterous Movement with Flexibility
As described in Section I-A, flexible manipulators have high DOFs and deformability. In this section, we show that the implemented manipulator can perform dexterous tasks that take advantage of these properties. First, the reaching task while contacting obstacles at several different positions in the intermediate link is shown in Fig. 11(a); the figure shows that reaching can be achieved by different configurations. In this task, the y-displacement of the caudal side is fixed at the contact point, but reaching is possible because of a total of two DOFs: the DOF of the head side motion by wire 1's traction and the DOF of the ventral side mechanism to change the length of the link. Because of the manipulator's deformability, the cranial side can be moved, even when it is in contact with an obstacle. The high-DOFs also allows the link length to be adjusted with a higher resolution. Second, as shown in Fig. 11(b), the implemented muscle-tendon arrangement was used to achieve the rolling pattern by sequentially pulling the ventral side while keeping the dorsal long muscle constant. The rolling pattern has the effect of reducing the moment applied to the base of the manipulator during the upward reaching of the head [19]. This is a good example of a task that takes advantage of high DOFs and deformability.

E. Role of Dorsal Muscles in Neck Movements
To demonstrate the role of the dorsal muscles over the entire neck in neck movement, we measured the joint angular velocity of the passive joints on the caudal side when the ventral mechanism was pulled in a predetermined pattern, as shown in Fig. 12(a). Fig. 12(b), and (c) show the time series of the joint angular velocities during the rolling pattern shown in Section IV-D. In Fig. 12(b), the ventral muscles were driven in sequence with a time delay of 0.1 s from the cranial side. In Fig. 12(c), they were driven simultaneously without a time delay. The sequence can be confirmed by focusing on the peak of the joint angular velocity in Fig. 12(b). As the example shows, for a flexible structure, the passive joints can be driven sequentially by a long muscle that runs through the entire structure. That is, a long muscle in a flexible structure provides dexterous movements, such as link length changes and rolling patterns. Furthermore, as shown in Fig. 12(c), the sequence occurs in the passive joints, even if the sequence is not strictly made. This is because the tension acts on the caudal passive joints via the dorsal wires, causing the head joints, which require the least torque for rotation, to move in sequence, regardless of the order of input. This means that when driving a more high-DOFs system, the number of independent actuators on the ventral side does not need to be correspondingly increased. This indicates the possibility of adding dexterity to a increasingly high-DOFs manipulator in a simpler way than the serialized underactuated system shown in Fig. 1(b).

F. Role of Joint Angle Limit in Neck Movement
This section compares and discusses the effects of joint angle limits on the behavior of flexible manipulators.
First, we consider the case of holding a posture against gravity in the lever pattern. Fig. 13(a) compares the neck posture when the dorsal wire is loosened and the neck is gradually swung down from the initial state, here with the dorsal wire pulled by the same amount for the presence and absence of a joint angle limit. This figure shows that the joint angle limit prevents excessive deformation of the caudal side of the neck because of wire tension and increases the reachable range of the tip compared with the case without it.
Next, we consider the role of the joint angle limits during neck movement in a rolling pattern. Fig. 13(b) shows a comparison of the behavior during the rolling pattern for the presence and absence of a joint angle limit. This figure shows that, in the absence of a joint angle limit, the cervical vertebrae are unable to maintain their posture. Fig. 13(c) shows the joint angles during the rolling pattern by the sequential commands with a time delay of approximately 1.0 seconds. Although there are exceptions due to the distribution of the joint range of motion, we can see that the joint angles (blue line) sequentially reached the joint angle limits (green line). That is, this movement pattern utilizes the constraints given by the joint angle limit. In other words, not only the elasticity between the joints shown by the blue line in Fig. 1(a), but also the joint angle limits are important as factors contributing to the coupling of each joint. Thus, the approach of actively using the joint angle limits for structural stability and for generating movement patterns is a new design principle for flexible manipulators.

V. CONCLUSION
A tendon-driven system is a useful approach for driving flexible structures. However, issues such as operational dexterity, structural stability, and modeling errors exist. For these issues, we proposed a design principle that applies muscle-tendon arrangement and joint angle limit based on the anatomy of an ostrich's neck. In particular, the schematic drawing of muscle and the cross-sectional views obtained by our dissection revealed regions where the muscle force acts. By comprehensively considering these findings, and the articulation structure and motor control of the avian neck, we proposed a novel mechanical system for an underactuated tendon-driven flexible manipulator. We also proposed a method to compensate for modeling errors by formulating ostrich neck movement patterns as a kinematic model and using this for feedback. The RobOstrich manipulator was capable of reaching movement with dexterity and structural stability. These results indicate the future feasibility of a servo system that is robust to environmental contact using visual feedback [23]. In this study, control laws to keep a constant dorsal muscle length and the effect of joint angle limits on behavior were also examined using a robot. These results provide biological insights that would be difficult to obtain by analysis alone, hence being called "Robotics-inspired biology" [24].

A. Fitting Method
To approximate the shape of the RobOstrich manipulator with the proposed model, we introduce the following evaluation function that takes into account the characteristics of deformation by wires: where α 1 to α 4 are the hyperparameters. The first and second terms represent the squared error of the distance of p T and p A corresponding to the tip position of the C14 cervical vertebrae connected by the manipulator tip and wire 2, respectively, in Fig. 14(a). The third term is the squared error of the point group formed by joints C8 to C11 and the midpoint p BC of BC, which is basis for variable x. The fourth term is the square error between the central angle θ m of BC and the angle θ r between C6 and C14, to which wires 1 and 2 have been fixed. By minimizing this evaluation function, the actual shape of the RobOstrich manipulator can be approximated by the proposed model. Fig. 14(b) shows an example of approximation by using this evaluation function. By using it in the proposed kinematics model, the characteristics of the deformation of the RobOstrich manipulator can be obtained.

B. Evaluation of Jacobian Matrix
As in Section IV-A, wire 1, wire 2, and the ventral mechanism were pulled independently for the initial posture Fig. 15(a). The posture during movement was successively approximated by the proposed model, and the predicted direction of travel φ could be  This indicates that the method that approximates the proposed model, especially in Fig. 15(a), and (b), and calculates (4)- (7) sequentially can predict the direction of head displacement more accurately than the method that calculates them feed-forwardly from the amount of wire pull. Based on the above results, the proposed kinematic model can be used to configure the feedback system to achieve reaching that is robust against modeling errors, as if operated by a human.