This article presents a research focused on developing musculoskeletal system for bio-inspired robotic systems. A musculoskeletal system is the fundamental structure that allows complex mobility of biological systems. This paper briefly describes the recently introduced twisted and coiled polymer (TCP) muscles and a novel design of musculoskeletal system based on ball and socket joint, as well as their application in a 3D printed humanoid robot. The challenge to develop such systems is multifaceted, including design, manufacturing, system integration, control methods, and energy usage. Some of the challenges in humanoid design are the degrees of freedom and the synergetic combination of hardware and software to perform a particular task. The other challenge is affordability of the platform. Most humanoids are very expensive. Since the TCP-based actuators are inexpensive and musculoskeletal systems inspired by biological systems are optimum for performance, they will address these problems. The bio-inspired ball and socket joint shown in the article can be cascaded to create complex robots, for example, for the shoulder joint of a humanoid.

## Article

A musculoskeletal system is the fundamental structure that allows complex mobility of biological systems.

Several research attempts have been made in the past to mimic this structure using synthetic materials for use in robotic systems. The challenge to develop such systems is multifaceted, including design, manufacturing, system integration, control methods and energy usage. The most important element of a musculoskeletal system is artificial muscles or actuators used in this system. Even though many types of actuators are proposed in the literature, most of them do not match the performance of natural muscles in all metrics such as force generation, strain output, frequency, power density, ease of control, and repeatability. This article briefly describes the recently introduced twisted and coiled polymer (TCP) muscles and a novel design of musculoskeletal system based on ball and socket joint, as well as their application in a 3-D printed humanoid robot. The musculoskeletal system can serve as a building block for bio-inspired systems that can be cascaded in various fashions to create complex robots.

## Synthesis of TCP Muscles and Structures for Robots

Twisted and coiled are polymer muscles are soft polymer muscles formed by inserting twists in a polymer precursor fiber such as polyethylene fishing line or nylon sewing thread (silver-coated nylon precursor) using a simple rotatory motor or coiling the fiber around a mandrel while it is pre-tensioned by a weight, followed by thermal treatment [1]. When heated electrothermally (resistive heating, by applying electrical power across the ends), the silver-coated TCP muscles contract, generating force/stress. The material is suitable to develop soft robots, assistive devices, prosthetics or orthotics, and humanoid robots. TCP muscles wrapped with carbon nanotubes (CNT) can be actuated electrothermally. It was shown that the muscles could sustain millions of cycles before failure [1]. Wrapping with CNT is not necessary, but it helps in heating the polymer due to the high conductivity of CNT. Silver-coated TCP material (without CNT) was used to develop a novel musculoskeletal system (shown in Figure 1). The muscles are arranged to actuate a ball and socket joint in two axes. Another two diagonal muscles can be integrated for the third rotation. Extremely twisted coiled polymer muscles could provide large strain (20-49%), large stress (1-35 MPa) and high mechanical work (up to 5.3 kW/kg) [1]. Therefore, it is worth investigating this material further for application in robotics.

The resistance of the TCP muscles changes during actuation, which can be detected by a microcontroller for sensing applications [1,2]. Therefore, the muscles have self-sensing capabilities and do not require external sensors. Since the muscles are inexpensive as compared with other actuators, they can be used for multiple purposes. The fundamental material properties are dependent on the synthesis technique (coiling speed, weight used, heat treatment, fiber alignment, annealing time, and precursor materials). There are currently few studies about the relationships between these parameters and performance. Therefore, experiments and theoretical modeling are required to establish the synthesis-performance relationships of TCP at various scales and domains (macro and micro).

## Soft Actuators for Biomimetic Robots

Actuators are the building blocks of many robots, and a fundamental understanding of their operation and construction is required to create novel bioinspired robots. Several soft biomimetic robots are presented in the literature, including hydrogen fuel-powered robotic jellyfish made out of MWCNT/SMA/Pt [3], and 3-D printed elastomeric tentacle structures integrated with shape memory alloy actuators [4]. The MWCNT/SMA/Pt is a composite muscle consisting of platinum catalyst-coated multi-wall carbon nanotube (MWCNT) sheets, wrapped on the surface of nickel-titanium (NiTi) shape memory alloy (SMA). SMAs are useful for soft robots. However, they are expensive (e.g., BMX150 costs $115/5m, equivalent to$3000/kg) compared with the TCP material (\$5/kg for the precursor fiber) presented in this article. Other actuators such as dielectric elastomers, conducting polymer, fluidic, hydraulic, hydrogel, and carbon nanotube actuators are in general the subjects of continued research to improve their performance.

## TCP Muscles—Electrically Activated

Recently, some research groups have presented experimental results of TCP muscles (referred to as coiled nylon in most papers) on various aspects such as variable stiffness structure [5], torsional actuation [6], and actuation using hot air [7]. We recently demonstrated [8] a contraction of 22% for a coiled monofilament fiber when heated/cooled by 25̊C and 95̊C water while lifting a 200 g weight for actuation of a robotic finger. However, actuation using resistive heating of the silver-coated muscle is easier for robotic applications.

We have conducted experiments on single ply (1-ply) muscle using resistive heating to actuate the muscle and obtain time domain experimental measurements using LabVIEW. We used a K-type thermocouple, an Omega LCL-010 load cell, and a Sharpe IR displacement sensor for the measurement of temperature, force, and displacement, respectively. Current and voltage were measured by NI modules and electrical power was provided to the muscle using computer controlled BK Precision (1687 B) power supply as shown in Figure 2.

We used five different values of power as shown in Figure 3a and performed experiments for two cycles. The corresponding temperature distribution is provided in Figure 3b, where the rise in temperature ranges from 60̊C to 150̊C. The Force-Displacement diagram is illustrated in Figure 3c, where the force has an almost linear relationship with the displacement, and has almost zero hysteresis. In Figure 3c, all the forces begin from ∼0.65 N due pre-straining of the muscle. Pre-strain is an important factor in performance and life of the muscle. The actuation of the 1-ply muscle reaches up to ΔL=18 mm displacement, which corresponds to 20% strain as shown in Figure 3d. Actuation strain is defined as ε = (ΔL/L) 100%, where ΔL is the displacement from initial position and L is the length of the actuator or the muscle before actuation (L= 90 mm).

Several researchers have reported results on TCP muscles, including a strain of 50% at 80 MPa using a fiber diameter of 0.5 mm [7], and 29% actuation at 4.1 MPa stress with regard to the coil cross-sectional area (26.8 MPa when normalized with the fiber diameter) using precursor fiber diameters of 188 μm and 296 μm [9]. Another report showed 10% actuation at 1 N force using a precursor fiber diameter of 720 μm [10]. In our experiments on 1-ply muscle, a 0.8 N force has been observed at maximum of 18 mm displacement (20% actuation strain), as can be seen in Figure 3c. The muscle for this test was prepared from a silver-coated precursor diameter of 180 μm and twisted and coiled under a 120 g load, resulting in a coiled diameter of 920 μm and length of 90 mm. Performance of the muscle is very much dependent on the way the muscle is synthesized, including the annealing process. For instance, 33% to 11.6% hysteresis were reported in [7]. But we have observed much less hysteresis loss, as can be observed from Figure 3c.

## Why TCP

The key parameters for comparison of artificial muscles are the free strain and blocking stress [11,12]. Figure 4 depicts some of the performance indices of suitable actuators for soft robots and humanoid robots in terms of stress-strain and energy per volume. In the plot, cylindrical SMA actuators showed the highest stress, greater than 100 MPa and energy density between 105-107 J/m3 (diagonal lines). In general, SMA actuators were the best actuators for low frequency applications in the last decades. However, this position is challenged by recent development in artificial muscle, specifically twisted and coiled polymer muscle, which is extremely inexpensive, compared to SMA and overcomes the limitations of SMA [1], [8], [12], [13]. As can be seen in Figure 4, the TCP muscle exhibits superb performance in stress-strain and energy density (diagonal line) graphs.

## Novel Musculoskeletal System Characterization

The musculoskeletal system shown earlier in Figure 1 was tested to generate multidimensional actuation. The design and prototype are illustrated in Figure 5a. Based on this design, we developed prototypes shown in Figure 5b. Figure 5b shows the prototype (ball and socket joint with cylindrical soft silicone support, Ecoflex® 00-30 hardness), which has the ability to twist in any angle. In another prototype, as shown in Figure 5c, the TCP muscles are integrated in parallel with the cylindrical silicone supports. The current prototype can reach a maximum bending angle of 300. The muscles were produced following a similar fabrication procedure as reported in [1]. Here 120 g was used as the dead weight during twist insertion. Then the coiled muscles were folded in the middle to make 2-ply muscles. The muscles after annealing and appropriate training can achieve around 6.5%∼14% actuation under a power of 0.14∼0.21 W/cm (note that this actuator is different from the one shown in Figure 3, 1-ply muscle). In order to actuate in two axes, 4 TCP muscles were crimped on both ends and then anchored in parallel to the bottom and top plates of the joints. The TCP muscles were placed in agonist/ antagonist pairs so that the joint rotation can be controlled by adjusting the power input to the muscles. The bio-inspired ball and socket joint can be cascaded to create complex robots as shown in CAD design in Figure 5d, e.g., 1 or 3 tentacle robots. Such robots could be used in underwater or terrestrial environments.

## Humanoids

In the areas of humanoids, robots have been developed in universities and research institutes. The actuators used in these robots are not inexpensive, not based on smart actuators, and not biomimetic. Some of the advanced humanoids include ASIMO, Robonaut, and HRP-4C. Therefore, more work is needed to make humanoids smarter and more affordable. Smart materials are responsive to external stimuli such as stress, temperature, electric field, magnetic field, humidity, and pH. They can be used as actuators (artificial muscles), sensors, and energy harvesting systems. We have made several efforts in creating humanoids using various smart actuation technologies: piezo-electric motor, conducting polymer, and shape memory alloy actuators. The latest humanoid is actuated by TCP muscles and uses additive manufacturing technology. Key scientihc challenges (synthesis, characterization and modeling) and performance of smart materials were described in our previous works [8,12,14]. Figure 6a is our humanoid robot, HBS-1, that has been developed using TCP muscles and other actuators. The TCP muscles are used for actuation of fingers (Figure 6d) of the robots [15] and the muscles can also be applied for facial muscles as shown in Figure 6b and 6c. Other actuation technologies have been investigated in the literature. However, not all of the requirements of cost, performance, complexity, and usability have been met.

## Humanoid Robot Applications and Outlook

Humanoid robots can assist human beings in numerous ways, from military applications and hrehghting to entertainment, socially assistive devices, medical studies, and childhood education. Soft actuators are showing excellent results for the development of these humanoids for cognitive studies or for training medical professionals. In addition, facially expressive robots are demonstrating encouraging results as therapeutic tools for children with Autism Spectrum Disorder (ASD). Various studies suggest that the design space of humanoid robots needs to be advanced in order to achieve conclusive results. Young children would like to interact with a humanoid robot as long as it is under their size. As shown in Figure 7a and 7b, two brothers (10 and 12 years old) enjoyed interacting with our humanoid HBS-1. They want the robot to have high capability just like Spiderman.

Some of the challenges in humanoid design are the degrees of freedom and the synergetic combination of hardware and software to perform a particular task. The other challenge is affordability of the platform. Most humanoids are very expensive. Since the TCP-based actuators are inexpensive and musculoskeletal systems inspired by biological systems are optimum for performance, they will address these problems. The bio-inspired ball and socket joint shown earlier in Figure 1 can be cascaded to create complex robots, for example, for the shoulder joint of a humanoid.

## Acknowledgments

The authors would like to acknowledge the support of the Office of Naval Research (ONR), Young Investigator Program, under the grant number N00014-15-1-2503.

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