Parallel Architectures for Humanoid Robots

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Article † Parallel Architectures for Humanoid Robots

Marco Ceccarelli 1,2,* , Matteo Russo 3 and Cuauhtemoc Morales-Cruz 1,4 1 LARM2: Laboratory of Robot Mechatronics, University of Roma Tor Vergata, Via del Politecnico 1, 00133 Rome, Italy; [email protected] 2 Beijing Advanced Innovation Center for Intelligent Robots and Systems, Beijing Institute of Technology, Beijing 100081, China 3 The Rolls-Royce UTC in Manufacturing and On-Wing Technology, University of Nottingham, Nottingham NG8 1BB, UK; [email protected] 4 Instituto Politécnico Nacional, GIIM: Group of Research and Innovation in Mechatronics, Av. Juan de Dios Bátiz, 07700 Mexico City, Mexico * Correspondence: [email protected] This paper is an extended version of our paper published in Marco, C.; Matteo, R. Parallel Mechanism † Designs for Humanoid Robots. In Robotics and Mechatronics; Kuo, C.H., Lin, P.C., Essomba, T., Chen, G.C., Eds.; Springer Nature: Cham, Switzerland, 2020; Volume 78, pp. 255–264.

Received: 11 August 2020; Accepted: 21 September 2020; Published: 23 September 2020

Abstract: The structure of humanoid robots can be inspired to human anatomy and operation with open challenges in mechanical performance that can be achieved by using parallel kinematic mechanisms. Parallel mechanisms can be identiﬁed in human anatomy with operations that can be used for designing parallel mechanisms in the structure of humanoid robots. Design issues are outlined as requirements and performance for parallel mechanisms in humanoid structures. The example of LARMbot humanoid design is presented as from direct authors’ experience to show an example of the feasibility and eﬃciency of using parallel mechanisms in humanoid structures. This work is an extension of a paper presented at ISRM 2019 conference (International Symposium on Robotics and Mechatronics).

Keywords: mechanism design; humanoid robots; biomimetic designs; parallel mechanisms; LARMbot

1. Introduction The first anthropomorphic humanoid robot, WABOT-1, was built at Waseda University, Tokyo, as part of the WABOT project (1970). WABOT-1 was a full-scale humanoid robot, able to walk, grasp and transport small object with its hands, and equipped with a vision system used for basic navigation tasks. The same research group later built WABOT-2 (1984) and WABIAN (1997), both biped humanoid robots, and is still active in the field [1]. Around 1986, Honda started to develop a biped platform that underwent through several stages, called “E” (1986–1993) and “P” (1993–1997) series, and led to the creation of ASIMO [2]. ASIMO was officially unveiled in 2000 and had a significant impact on the media all around the world. It is a humanoid platform with an advanced vision and navigation system, able to interpret voice or gesture commands and to move autonomously with a semi-dynamic walking mode. In 2008, Aldebaran Robotics launched NAO, a programmable humanoid robot that is now the standard platform for several robotics competitions, such as the RoboCup Standard Platform League [3,4]. NAO has been the most widespread robot in academic and scientific usage, used to teach and develop advanced programming and control in educational and research institutes all around the world. In 2013, Boston Dynamics announced the Atlas robot, a biped robot capable of complex dynamic tasks, such as running, moving on snow, performing a backflip, balancing after being hit by projectiles or jumping on one leg [5].

Robotics 2020, 9, 75; doi:10.3390/robotics9040075 www.mdpi.com/journal/robotics Robotics 2020, 9, 75 2 of 16

Several other humanoid structures have been designed both by academy and industry with a variety of solutions as platforms for research and applications for service (as for example in assistance to humans, entertainment, guide operations), exploration, human-robot interaction and learning. Some additional examples include: iCub [6], and for research on learning; WALK-MAN, [7], which is used as a rescue robot for unstructured environments; Pepper, [8], which is used for investigations on human-robot interaction; Ami, [9], which is designed for applications in Domotics; REEM-B, [10], which is designed as service robot for general human assistance; ARMAR, [11,12], which is used as a collaborative robot in Domotics tasks. While there has been a huge development in the control of these robots, they all share a common body architecture, which has not evolved much during time. In fact, most of them are based on a serial kinematic chain with spherical-revolute-universal (SRU) joints for their limbs. This mechanical structure is fairly easy to manufacture and control, while offering a large workspace for its size. However, serial architectures are outperformed by parallel mechanisms in accuracy, speed, stiffness and payload. Parallel manipulators, also named parallel kinematic machines (PKM), are closed-loop mechanisms that are characterized by high accuracy, rigidity and payload [13]. A parallel manipulator is defined as a mechanical system that allow a rigid body, called from now on an end-effector, to move with respect to a fixed base by means of two or more independent kinematic chains. Very few research groups have proposed robotic limbs with a parallel architecture. As reported in [14], the first robotic legs with parallel architecture were developed in Japan. The first one was the ParaWalker robot, developed at Tokyo Institute of Technology in 1992, while the Waseda Leg (WL) WL-15 was built in 2001 at the Takanishi laboratory of Waseda University, followed by the WL-16 and the WL-16R series from 2002 to 2007 [15]. The last version of the Waseda Leg is the WL-16RV. The WL robots are biped walking chairs, whose legs are based on the architecture of the Gough platform. The WL design inspired other teams in designing novel biped robots built on parallel mechanisms, such as the Reconfigurable Quadruped/Biped Walking Robot of Yanshan University, which is built on four legs with three identical universal-prismatic-universal limbs (3UPU) each. The LARMbot [16–21] was designed as a low-cost, user-oriented leg for a service humanoid robot. Its leg is designed as a 3UPR PKM. Gao used similar lower-mobility parallel legs for a hexapod robot [22–24]. The main drawback for most of these legs, however, is the small dimension of their workspace, which allows for a very small step size when compared to the human one [25–28]. In order to characterize the mechanical performance of robotic limbs that have been developed in the last few decades, the main parameters of representative humanoid robots are listed in Table1[ 27].

Table 1. Characteristic parameters of biped robots.

Name Type Weight [kg] Height [mm] Step [mm] Speed [mm s 1] DoF [-] Year · − MELTRAN II Serial 4.7 450 120 200 3 1989 HRP-2 Serial 58.0 1540 - - 6 2003 WABIAN-2 Serial 64.5 1530 350 360 7 2005 WL-16RV Parallel 75.0 1440 200 200 6 2008 WABIAN-2RIII Serial 64.0 1500 500 520 7 2009 HUBO2 Serial 45.0 1300 - 410 6 2009 ASIMO Serial 54.0 1300 410 750 6 2011 BHR5 Serial 63.0 1620 - 440 6 2012 ATLAS Serial 150.0 1800 - - 6 2013 NAO V5 Serial 5.4 574 80 160 6 2016

Each robot is classiﬁed according to its kinematic architecture (serial or parallel), system weight and height, maximum step size, maximum gait speed, degrees-of-freedom of each leg and year of production. As reported in Table1, most of the existing robots have 6-DoFs serial limb architectures. The most famous humanoid robots, such as ASIMO and NAO, are all based on this kinematic scheme. The size and weight of the robots did not change signiﬁcantly with the years, and even the step size and speed are in a reduced range of values when compared to the size of the robot. Most of the Robotics 2020, 9, x 3 of 17

Each robot is classified according to its kinematic architecture (serial or parallel), system weight and height, maximum step size, maximum gait speed, degrees-of-freedom of each leg and year of production. As reported in Table 1, most of the existing robots have 6-DoFs serial limb architectures. TheRobotics most2020 famous, 9, 75 humanoid robots, such as ASIMO and NAO, are all based on this kinematic scheme.3 of 16 The size and weight of the robots did not change significantly with the years, and even the step size and speed are in a reduced range of values when compared to the size of the robot. Most of the advancements are in the performance of control and gait planning, while the mechanical design has advancements are in the performance of control and gait planning, while the mechanical design has not evolved. Furthermore, the payload capacity of the current structures of humanoid robots is rather not evolved. Furthermore, the payload capacity of the current structures of humanoid robots is rather small (for example, NAO can lift only 0.15 kg per arm), and they can be often operated with poor small (for example, NAO can lift only 0.15 kg per arm), and they can be often operated with poor dynamics and stiﬀness. Therefore, challenging design issues can be still identiﬁed in improving or dynamics and stiffness. Therefore, challenging design issues can be still identified in improving or designing structures of humanoid robots and parallel mechanisms can be considered a solution or an designing structures of humanoid robots and parallel mechanisms can be considered a solution or an alternative to achieve a mechanical design with better performance in accuracy, payload and dynamics, alternative to achieve a mechanical design with better performance in accuracy, payload and not only mimicking human capabilities. dynamics, not only mimicking human capabilities. 2. Human Anatomy with Parallel Mechanisms 2. Human Anatomy with Parallel Mechanisms Humanoids are designed with structures and operations replicating human ones. Human nature Humanoids are designed with structures and operations replicating human ones. Human nature has a complex design in structure composition, with several kinds of material and architectures that has a complex design in structure composition, with several kinds of material and architectures that humanoid design can replicate only very partially. The most referenced part of human anatomy for humanoid design can replicate only very partially. The most referenced part of human anatomy for humanoid robot structures is the skeleton system, which inspires solutions mainly with rigid links in humanoid robot structures is the skeleton system, which inspires solutions mainly with rigid links in serial kinematic chain architectures. However, considering that the functionality of human movable serial kinematic chain architectures. However, considering that the functionality of human movable parts is mainly due to a combined/integrated structure of bones and muscles, the reference structure for parts is mainly due to a combined/integrated structure of bones and muscles, the reference structure humanoid robot design can be considered a parallel architecture that combines bones as rigid movable for humanoid robot design can be considered a parallel architecture that combines bones as rigid links and muscles as linear actuators. Figure1 summarizes such an understanding by looking at the movable links and muscles as linear actuators. Figure 1 summarizes such an understanding by looking bone skeleton structure (Figure1a) that, together with the muscle complex (Figure1b), can give a at the bone skeleton structure (Figure 1a) that, together with the muscle complex (Figure 1b), can give model of functioning mechanisms with parallel mechanisms (Figure1c). The antagonist functioning a model of functioning mechanisms with parallel mechanisms (Figure 1c). The antagonist functioning of muscles is characterized by the fact that the muscles mainly act with pulling actions when they of muscles is characterized by the fact that the muscles mainly act with pulling actions when they are are contracted, and therefore full mobility requires alternated actions of two muscles in pulling and contracted, and therefore full mobility requires alternated actions of two muscles in pulling and releasing. For complex motions, such as 3D movements, a bone is actuated by a complex group of releasing. For complex motions, such as 3D movements, a bone is actuated by a complex group of muscles that still control the operation through antagonist functionality. muscles that still control the operation through antagonist functionality.

(a) (b) (c)

FigureFigure 1. 1.TheThe anatomy anatomy of ofhuman human body: body: (a) ( askeleton) skeleton structure; structure; (b ()b muscle) muscle complex; complex; (c) ( ca) amodel model representingrepresenting the the functionalit functionalityy with with parallel parallel mechanisms. mechanisms.

Thus, although a basic principle can be still referred to the example in Figure1, human anatomy can be of diﬃcult replication in eﬃcient compact designs for humanoid robots. However, the inspiration from human anatomy for designs with parallel mechanisms can be summarized in solutions that are characterized by two platforms with relative motion, which are connected and actuated by a number Robotics 2020, 9, x 4 of 17

Thus, although a basic principle can be still referred to the example in Figure 1, human anatomy can be of difficult replication in efficient compact designs for humanoid robots. However, the inspiration from human anatomy for designs with parallel mechanisms can be summarized in Robotics 2020, 9, 75 4 of 16 solutions that are characterized by two platforms with relative motion, which are connected and actuated by a number of pairs of linear actuators working either independently (as rigid variable links)of pairs or in of antagonism linear actuators (as cable-driven working either links). independently A central rigid (as link, rigid replicating variable links)the bone or instructure antagonism and functionality,(as cable-driven can links). be included A central in rigidthe parallel link, replicating mechanism the bonedesign structure both to and keep functionality, the size and can the be loadincluded capability. in the parallel mechanism design both to keep the size and the load capability. InIn particular, particular, Figure Figure 2 givesgives anan exampleexample of suchsuch anan inspirationinspiration from human anatomy, withwith a parallelparallel architecture architecture of of bones bones and and muscles muscles for for designing designing a a movable movable arm arm with with a a parallel parallel mechanism mechanism thatthat is is based based on on the the antagonist antagonist actuation actuation of of a a pair pair of of muscles muscles for for a a planar planar motion. motion. As As per per the the forearm forearm motionmotion in in the the sagittal sagittal arm arm plane plane due due to to the the elbow elbow arti articulation,culation, Figure Figure 2 shows a solution with a central central rigidrigid link link L L that that is is connected connected the the platforms platforms with with revo revolutelute joints joints whereas whereas the the actuation actuation is is given given by by two two variablevariable cable cable links links l l11 andand l l22. .with with revolute revolute joints joints yet. yet. As As in in Figure Figure 22b,b, ll22 shortens,shortens, simulating simulating the the contractioncontraction of of the the muscle, muscle, while while l1 l1 isis stretched stretched for for the the release release of of the the corresponding corresponding antagonist antagonist muscle. muscle.

(a) (b)

FigureFigure 2. AnAn exampleexample of of parallel parallel architectures architecture withs with antagonist antagonist functioning: functioning: (a) arm (a in) humanarm in anatomy;human anatomy;(b) a replicating (b) a replicating parallel mechanism. parallel mechanism.

FigureFigure 33 showsshows an an example example of of modelling modelling of theof th complexe complex structure structure of bones of bones and muscles and muscles in a human in a humantrunk, intrunk, Figure in3 a,Figure for designing 3a, for designing a humanoid a humanoid trunk, as in trunk, Figure as3b, in as Figure based 3b, on parallelas based mechanisms on parallel mechanismswith the above-mentioned with the above-mentioned design. In particular, design. In the particular, central rigid the central link L canrigid be link designed L can be with designed a serial withchain a ofserial links chain Li replicating of links L thei replicating vertebras, the which vertebras, are connected which byare sphericalconnected joints by spherical or 2-DOF joints revolute or 2-DOFjoints inrevolute a suitable joints number in a suitable to ensure number the required to ensure ranges the required of flexion ranges and torsion.of flexion The and complex torsion. of The the complexmuscles canof the be muscles replicated can with be areplicated suitable number with a ofsuitable couples number of antagonist of couples variable of antagonist cable links, variable such as cablel1 and links, l2, to such give as a requiredl1 and l2, mobilityto give a torequired the shoulder mobility upper to the platform shoulder with upper respect platform to the with waist respect lower toplatform. the waist The lower number platform. of those The couples number of of cable those links couples can beof limitedcable links to only can four,be limited and their to only actuation four, andcan their be programmed actuation can to be give programmed some other motionto give some capability other when motion driven capability in a non-antagonist when driven in mode. a non- antagonistThe leg mode. structure in Figure4 can be aimed to the locomotor part of a humanoid robot, with a leg mobility with a large range of motion and a large payload capacity, due to the synergy of the action of the bones and muscle complex. This characteristic can be preserved by using the above-mentioned concept of having the bone load-supporting structure replicated by a central rigid link and the platform relative mobility ensured by the pulling action of the cables working. In addition, the human leg anatomy of the leg-shank structure can be preserved by conceiving two similar parallel mechanisms in series with the mobile platform of the upper-leg part as the fixed platform for the mobile shank platform. The mobility can be designed with a proper number of couples of antagonist cable links as per a required mobility. Thus, the upper-leg parallel mechanism can be designed to give 3 DOFs to the mobile knee platform with a central rigid link La and four cable links l1, l2, l3, l4, which can be activated to give planar motions in sagittal and traversal anatomical planes and even a torsion motion as per a hip joint mobility when the four cables are activated in cooperation (not in antagonism mode). Similarly, the shank motion can be limited to two cables l5, l6, for the sagittal motion of the end-effector Robotics 2020, 9, x 5 of 17

Robotics 2020, 9, 75 5 of 16

(a) (b) ankle platform that is connected to the knee platform by a rigid link Lb. Additional cable links l6, l7 can be providedFigure 3. Trunk to provide structure: the twist(a) in motionhuman anatomy; for the ankle (b) in platform.a replicating parallel mechanism. Robotics 2020, 9, x 5 of 17 The leg structure in Figure 4 can be aimed to the locomotor part of a humanoid robot, with a leg mobility with a large range of motion and a large payload capacity, due to the synergy of the action of the bones and muscle complex. This characteristic can be preserved by using the above-mentioned concept of having the bone load-supporting structure replicated by a central rigid link and the platform relative mobility ensured by the pulling action of the cables working. In addition, the human leg anatomy of the leg-shank structure can be preserved by conceiving two similar parallel mechanisms in series with the mobile platform of the upper-leg part as the fixed platform for the mobile shank platform. The mobility can be designed with a proper number of couples of antagonist cable links as per a required mobility. Thus, the upper-leg parallel mechanism can be designed to give 3 DOFs to the mobile knee platform with a central rigid link La and four cable links l1, l2, l3,l4, which can be activated to give planar motions in sagittal and traversal anatomical planes and even a torsion motion as per a hip joint mobility when the four cables are activated in cooperation (not in (a) (b) antagonism mode). Similarly, the shank motion can be limited to two cables l5, l6, for the sagittal motion of theFigureFigure end-effector 3.3. Trunk structure:structure:ankle platform (aa)) inin humanhuman that is anatomy;anatomy; connected ((bb)) ininto aa the replicatingreplicating knee platform parallelparallel mechanism. mechanism.by a rigid link Lb. Additional cable links l6, l7 can be provided to provide the twist motion for the ankle platform. The leg structure in Figure 4 can be aimed to the locomotor part of a humanoid robot, with a leg mobility with a large range of motion and a large payload capacity, due to the synergy of the action of the bones and muscle complex. This characteristic can be preserved by using the above-mentioned concept of having the bone load-supporting structure replicated by a central rigid link and the platform relative mobility ensured by the pulling action of the cables working. In addition, the human leg anatomy of the leg-shank structure can be preserved by conceiving two similar parallel mechanisms in series with the mobile platform of the upper-leg part as the fixed platform for the mobile shank platform. The mobility can be designed with a proper number of couples of antagonist cable links as per a required mobility. Thus, the upper-leg parallel mechanism can be designed to give 3 DOFs to the mobile knee platform with a central rigid link La and four cable links l1, l2, l3,l4, which can be activated to give planar motions in sagittal and traversal anatomical planes and even a torsion motion as per a hip joint mobility when the four cables are activated in cooperation (not in antagonism mode). Similarly, the shank motion can be limited to two cables l5, l6, for the sagittal motion of the end-effector ankle platform that is connected to the knee platform by a rigid link Lb. Additional cable links l6, l7 can be provided to provide the twist motion for the ankle platform.

(a) (b)

FigureFigure 4. 4.LegLeg structure: structure: (a) (ina) inhuman human anatomy; anatomy; (b) ( bin) ina replicating a replicating parallel parallel mechanism. mechanism.

TheThe examples examples in inFigures Figures 2–42– 4give give conceptual conceptual ki kinematicnematic designs designs of of the the idea idea of of using using parallel parallel cable-drivencable-driven mechanisms mechanisms for for replicating replicating the the human human anatomy anatomy made made of of bones and muscle complexescomplexes in a design of humanoid robots or parts of them. Figure4 is an example of a combination of parallel mechanisms for the leg structure and how they can be assembled in series.

3. Requirements and Performance for Humanoid Robots Humanoid robots are aimed at replicating/mimicking human operations mainly in locomotion, manipulation and sensing for human-like tasks. Figure5 summarizes those main aspects that should be considered for design and operation in mimicking human nature and its functionality, making a humanoid solution eﬃcient, durable and functional, with even better/diﬀerent performance than those of humans. (a) (b)

Figure 4. Leg structure: (a) in human anatomy; (b) in a replicating parallel mechanism.

The examples in Figures 2–4 give conceptual kinematic designs of the idea of using parallel cable-driven mechanisms for replicating the human anatomy made of bones and muscle complexes

Robotics 2020, 9, x 6 of 17 in a design of humanoid robots or parts of them. Figure 4 is an example of a combination of parallel mechanisms for the leg structure and how they can be assembled in series.

3. Requirements and Performance for Humanoid Robots Humanoid robots are aimed at replicating/mimicking human operations mainly in locomotion, manipulation and sensing for human-like tasks. Figure 5 summarizes those main aspects that should be considered for design and operation in mimicking human nature and its functionality, making a Roboticshumanoid2020, 9solution, 75 efficient, durable and functional, with even better/different performance 6than of 16 those of humans.

Figure 5. Main requirements for mechanical design and functionality of humanoid robots. Figure 5. Main requirements for mechanical design and functionality of humanoid robots.

In particular,particular, locomotion locomotion requirements requirements can becan obtained be obtained by analyzing by analyzing sizing issues sizing and functionalityissues and features.functionality Fundamental features. Fundamental attention can attention be addressed can be to legaddressed size for to and leg as size function for and of as the function required of step the sizerequired and vicestep versa.size and In addition,vice versa. speed In addition, data can speed be a characteristicdata can be a ofcharacteristic the prescribed of the task prescribed and can a fftaskect theand previouscan affect mentioned the previous aspect. ment Allioned together aspect. they All can together contribute they to design can contribute leg workspace, to design in order leg toworkspace, replicate thein order area ofto mobilityreplicate ofthe a humanarea of leg,mobility which of isa usuallyhuman characterizedleg, which is usually by suitable characterized values of stepby suitable length andvalues step of height. step length In addition, and step the height. locomotion In addition, can be performedthe locomotion in several can be modes performed just like in humans,several modes such as just walking, like humans, running andsuch jumping, as walking, with characteristicrunning and performancejumping, with in terms characteristic of speed andperformance motion smoothness. in terms of Amongspeed and practical motion requirements, smoothness. payload Among capability practical pays requirements, a fundamental payload role, notcapability only in pays sustaining a fundamental the weight role, of thenot full only humanoid, in sustaining but alsothe weight considering of the the full loads humanoid, and actions but also that theconsidering leg locomotor the loads will and have actions to collaborate that the with.leg locomotor A locomotion will have system to collaborate must be provided with. A with locomotion control softwaresystem must and hardware,be provided as wellwith ascontrol motion software strategies an withd hardware, proper path as well planning as motion and leg strategies coordination with forproper balancing path planning during bipedal and leg operations. coordination for balancing during bipedal operations. Similarly, thethe design design and and functionality functionality of manipulationof manipulation system system of a humanoidof a humanoid robot canrobot be guidedcan be byguided requirements by requirements in terms in of sizesterms and of sizes operation and oper performance.ation performance. Once the sizeOnce is defined,the size theis defined, constraints the forconstraints the arm for workspace the arm workspace and mobility and can mobility be defined can be to includedefined eachto include point each that thepoint arm that can the reach arm andcan allreach the and configurations all the configurations in which thatin which point that can poin be reachedt can be (with reached diff erent(with orientationsdifferent orientations for different for manipulationdifferent manipulation tasks). Accuracy tasks). andAccuracy dexterity and are dexterity characteristics are characteristics that can be dictatedthat can bybe thedictated task but by alsothe bytask the but flexibility also by the in operation flexibility that in operation can be expected that can by be the expected use of the by robot the use humanoid, of the robot The humanoid, payload of theThe armpayload structure of the should arm structure be enough should to support be enough a variety to support of human-like a variety manipulation of human-like tasks, manipulation which can betasks, linked which with can a good be linked accuracy with and a good repeatability. accuracy Manipulation and repeatability. capability Manipulation should also capability be characterized should inalso terms be characterized of dexterity, asin terms expressed of dexterity, by multiple as expressed reachable by arm multiple configurations reachable with arm suitable configurations motion andwith dynamicssuitable motion characteristics. and dynamics Motion characteristics. planning is alsoMotion a practical planning aspect, is also coming a practical from aspect, synergy coming with thefrom control synergy design with the and control motion design programming, and motion with programming, issues that with can beissues determinant that can be in determinant the design andin the functionality. design and functionality. Finally, the extremityFinally, the of extremit an arm,y suchof an asarm, a hand such oras a grasping hand or systems,grasping needssystems, to be considered as part of the problems for a well-integrated solution in manipulations, including grasp actions.

Sensing in humanoid robots can be considered as being integrated with the capabilities in locomotion and manipulation, as well as additional features, which are nonetheless based on the biomechanics of the structure and their operation, so that sensor equipment is needed with characteristics and composition, as outlined in Figure5, for the main human-like operation. Those sensors can be useful for the motion and action of a humanoid at proper levels of performance, as well as for monitoring and supervision purposes. Inertial measurement units (IMUs) are useful to have a feedback on the human-like motion, in order to react to external forces or unbalanced Robotics 2020, 9, 75 7 of 16 conﬁgurations with a proper balancing motion. Important sensing is also related to force detection, both in manipulation and locomotion, with or without further control feedbacks. Sensors are signiﬁcant in grasping tasks that require tactile capability. Image recognition is a sense that makes a humanoid aware of the environment and cameras are needed for autonomous navigation through obstacle detection, and for area inspection through object recognition. Other common sensors in humanoid robots are haptic sensors to perceive the interaction of a humanoid robot with the environment. In addition, a humanoid robot should be equipped with sensors that are sources of information for the task under execution. Referring to an average human characterization, Table2 lists an example of numerical evaluation of design requirements for humanoid design, as referred to in the requirements in Figure5, as linked to solutions with parallel mechanisms.

Table 2. Requirements for humanoid designs as shown in Figure5,[10–12].

Characteristics Human Reference Value Expected Value in Humanoids Step length (natural) <94% leg height 50–100% leg height Step length (fast) >116% leg height 50–125% leg height Speed <105 steps per minute 50–120 steps per minute Leg mobility 6 D.o.F. >5 D.o.F. Leg payload capacity <200% body weight >100% body weight Arm mobility 6 D.o.F. >6 D.o.F. Arm payload capacity <100% body weight >50% body weight Torso ﬂexion/extension 30–45◦ 10–30◦ Torso lateral bending <40◦ <30◦ Power consumption <6.00 W/kg <10.0 W/kg

The expected performance in Table2 is estimated considering design solutions with parallel architectures, enhancing the whole humanoid design with minimum–maximum ranges that can satisfy task characteristics and/or performance operation in other aspects. Design solutions with proper dimensions and range of motion can be deﬁned by using computations for the corresponding model and formulation of the kinematics and force transmission of parallel manipulators. In particular, referring to the antagonistic operation mode in the conceptual scheme in Figure6a, the kinematics of the operation can be formulated with loop-closure equations as

A0Ai + li + BiB0 = L; A0Aj + lj + BjB0 = L (1) where the design parameters are the position of the spherical or revolute joints Ai, Aj, Bi and Bj, and the length of the central link L, as well as the motion parameters given by parallel limb lengths li and lj. Given the antagonistic functioning of the system, a single equation for each antagonistic pair of actuators is enough to fully characterize the kinematics of the pair, and the length of the remaining limb can be obtained as a function of its antagonist. A static or dynamic model can be used to evaluate the actuation forces in the linear actuators or equivalent cable-driven structures, and the equilibrium to translation can be given by

Fi + Fj + R + P = 0 (2) where the equilibrium to rotation can be expressed as

B B F + B B F + M = 0 (3) i 0 × i j 0× j where Fi and Fj are the actuation forces in the i-th and j-th limb respectively, R is the reaction in the central link and P and M represent external forces and moments applied to the lower platform, as shown in Figure6b. Robotics 2020, 9, 75 8 of 16

The above formulation can be further elaborated for speciﬁc cases, as shown in the LARMbot example in Section4, which is controlled with kinematic and static models that are developed from Equations (1)–(3), as outlined with details in [17]. Robotics 2020, 9, x 8 of 17

(a) (b)

FigureFigure 6. 6.A A general general scheme scheme of of a parallela parallel mechanism mechanism with with antagonistic antagonistic operation operation modes: modes: (a )(a kinematic) kinematic diagram;diagram; (b ()b free-body) free-body diagram diagram of of the the lower lower platform. platform.

4. An IllustrativeA static or dynamic Example model can be used to evaluate the actuation forces in the linear actuators or equivalentA direct cable-driven experience ofstructures, the authors and inthe using equilibrium parallel to mechanisms translation can in humanoid be given by designs refers to LARMbot design. The LARMbot humanoid𝑭𝒊 +𝑭𝒋 +𝑹+𝑷=𝟎 robot has been developed in the last decade(2) with contribution of several researchers at LARM laboratory of University of Cassino and South Latium,where [the29, 30equilibrium]. The LARMbot to rota design,tion can shown be expressed in Figure as7 , is a service robot for autonomous walking and manipulation tasks, with basic performance𝑩𝑩𝟎 𝑭𝒊 +𝑩 in mimicking𝑩𝟎 𝑭𝒋 +𝑴=𝟎 structure but functionality of humans.(3) As pointed out in [16,29], a first full prototype of LARMbot was assembled in 2015, while a second where Fi and Fj are the actuation forces in the i-th and j-th limb respectively, R is the reaction in the version, LARMbot II, with a different leg architecture [16,17] is now available for lab testing at LARM2 central link and P and M represent external forces and moments applied to the lower platform, as in University of Rome “Tor Vergata”. shown in Figure 6b. The LARMbot design is characterized by two main parallel mechanism systems, namely one for The above formulation can be further elaborated for specific cases, as shown in the LARMbot leg-locomotion and one for arm-trunk. The prototype has been built by using commercial components example in Section 4, which is controlled with kinematic and static models that are developed from available off-the-shelf and by manufacturing other parts with 3D printing, in order to get a system that is Equations (1)–(3), as outlined with details in [17]. 850 mm tall with a weight less than 3.70 kg. Its payload capability is 0.85 kg for manipulation, and more than 3 kg for the torso/leg operation, whose parallel architectures give a structure that is considerably 4. An Illustrative Example stronger than traditional humanoids. The payload to weight ratio is 0.23 for manipulation and 0.81 for weightlifting,A direct experience which is considerablyof the authors larger in using than parallel in other mechanisms existing humanoid in humanoid robots. designs For example, refers to theLARMbot similar-sized design. NAO The humanoid, LARMbot which humanoid is designed robot with has serial been kinematic developed architectures, in the last has decade a payload with tocontribution weight ratio of of several only 0.03 researcher [3,4]. Furthermore,s at LARM LARMbotlaboratory is of energy-e Universiffitycient, of Cassino with a peakand South 20 W powerLatium, consumption[29,30]. The inLARMbot LARMbot design, II prototype, shown as in tested Figure in 7, [17 is]. a service robot for autonomous walking and manipulationThe trunk tasks, design with in Figurebasic performance8a is based onin mi themicking CAUTO structure solution, but [ functionality18], as an underactuated of humans. As cable-drivenpointed out serial-parallel in [16,29], a mechanismfirst full prototype whose kinematic of LARMbot scheme was is assembled shown in Figure in 2015,8b aswhile referring a second to theversion, conceptual LARMbot design II, in Figurewith a3 .different The LARMbot leg architecture trunk is composed [16,17] is of now parallel available mechanisms for lab with testing four at cablesLARM2 and in a University central underactuated of Rome “Tor serial Vergata”. chain whose extremity joints are fixed in the center of the mobile shoulder plate of the parallel mechanism. It is a 4SPS-(3S) parallel mechanism with 4 DOFs, which are actuated by the four motors for varying the length of each cable. The mechanism is inspired by the human torso bone-muscle complex as in the scheme in Figure3b, with a serial-kinematic compliant spine in the center as a 3S chain, shown in Figure8b. The cables act as antagonist muscles for motion control in coordination of the cable pairs, according to the kinematic model in Equation (1), with L representing the spine structure. In addition to its main function of load-supporting structure,

Robotics 2020, 9, 75 9 of 16

the LARMbot trunk can be used with its controlled motion to enhance and support walking balance too, as outlined in [17]. Robotics 2020, 9, x 9 of 17

(a) (b)

FigureFigure 7. 7. LARMbotLARMbot II II humanoid humanoid with with parallel parallel mechanisms: mechanisms: ( (aa)) a a CAD CAD model; model; ( (bb)) a a prototype. prototype. Robotics 2020, 9, x 10 of 17 The LARMbot design is characterized by two main parallel mechanism systems, namely one for leg-locomotion and one for arm-trunk. The prototype has been built by using commercial components available off-the-shelf and by manufacturing other parts with 3D printing, in order to get a system that is 850 mm tall with a weight less than 3.70 kg. Its payload capability is 0.85 kg for manipulation, and more than 3 kg for the torso/leg operation, whose parallel architectures give a structure that is considerably stronger than traditional humanoids. The payload to weight ratio is 0.23 for manipulation and 0.81 for weightlifting, which is considerably larger than in other existing humanoid robots. For example, the similar-sized NAO humanoid, which is designed with serial kinematic architectures, has a payload to weight ratio of only 0.03 [3,4]. Furthermore, LARMbot is energy-efficient, with a peak 20 W power consumption in LARMbot II prototype, as tested in [17]. The trunk design in Figure 8a is based on the CAUTO solution, [18], as an underactuated cable-driven serial-parallel mechanism whose kinematic scheme is shown in Figure 8b as referring to the conceptual design in Figure 3. The LARMbot trunk is composed of parallel mechanisms with four cables and a central(a) underactuated serial chain whose(b) extremity joints are fixed in (thec) center of the mobile shoulder plate of the parallel mechanism. It is a 4SPS-(3S) parallel mechanism with 4 DOFs, FigureFigure 8. 8.Spinal Spinal structure: structure: (a ()a human) human spine spine with with ligaments; ligaments; (b )( ab) scheme a scheme for spine-torsofor spine-torso design; design; (c) which are actuated by the four motors for varying the length of each cable. The mechanism is inspired LARMbot(c) LARMbot spine-torso spine-torso prototype. prototype. by the human torso bone-muscle complex as in the scheme in Figure 3b, with a serial-kinematic compliantTheThe leg-locomotor leg-locomotorspine in the center design design as is shownais 3S shown chain, in Figurein shown Figure9, with in 9, Figure with the conceptual the 8b. conceptual The cables design design act schemes as antagonistschemes of two of legs muscles two with legs forhumanwith motion human anatomy control anatomy inspiration, in inspiration,coordination whereas whereas itsof operational the itscabl operate characteristicspairs,ional accordingcharacteristics are presentedto the are kinematicpresented in [19]. The inmodel design[19]. Thein is Equationdesign is (1), inspired with byL representingthe human upper-leg the spine structure structure. as inIn Figureaddition 9a, towhich its mainrefers function to a single of parallelload- supportingmechanism structure, in Figure the 4, as LARMbot per gross trunkfunctionality. can be usedThree with actuators its controlled represent motion the main to muscleenhance groups and supportof the upperwalking leg, balance namely too, hamstrings, as outlined quadriceps in [17]. and adductors. Each leg is designed as a 3UPR lower-mobility parallel mechanism, which is shown in Figure 9b as connecting the hip in the waist platform to the ankle mobile platform. It is actuated by three linear actuators in the links, which converge to a single point of the ankle platform. A special joint design ensures the point convergence of the three linear actuators, resulting in a workspace larger than similar parallel manipulators, as well as human-like mobility, which is also characterized by no singular configurations, as discussed in [20,21]. With reference to Figures 6 and 9b, the kinematics of each leg can be expressed as

𝑩𝟎 = 𝑨𝟎𝑨 +𝒍𝒊 (4)

where Ai represents the position of the spherical joints on the upper platform, A0 is the center of the upper platform, B0 is the point of convergence of the three limbs and the motion parameters are given by linear actuator lengths li. This formulation can be obtained from Equation (1) by imposing the convergence of the limbs and removing the fixed-length central limb, and it can be used to control the motion of the locomotion system of the robot, as explained with details in [19–21].

(a) (b) (c)

Figure 9. Leg structure: (a) human leg with muscles; (b) a scheme for leg design; (c) LARMbot leg locomotor prototype.

Robotics 2020, 9, x 10 of 17

(a) (b) (c)

Figure 8. Spinal structure: (a) human spine with ligaments; (b) a scheme for spine-torso design; Robotics(c2020) LARMbot, 9, 75 spine-torso prototype. 10 of 16

The leg-locomotor design is shown in Figure 9, with the conceptual design schemes of two legs inspiredwith human by the anatomy human upper-leginspiration, structure whereas as inits Figureoperat9ionala, which characteristics refers to a single are presented parallel mechanism in [19]. The indesign Figure is4 ,inspired as per gross by the functionality. human upper-leg Three actuators structure representas in Figure the 9a, main which muscle refers groups to a single of the parallel upper leg,mechanism namely hamstrings,in Figure 4, as quadriceps per gross andfunctionality. adductors. Three Each actuators leg is designed represent as athe 3UPR main lower-mobility muscle groups parallelof the mechanism,upper leg, namely which ishamstrings, shown in Figure quadriceps9b as connecting and adductors. the hip inEach the waistleg is platformdesigned to as the a ankle3UPR mobilelower-mobility platform. parallel It is actuated mechanism, by three which linear is actuators shown in theFigure links, 9b which as connecting converge the to ahip single in the point waist of theplatform ankle platform.to the ankle A special mobile joint platform. design It ensures is actuated the point by three convergence linear actuators of the three in linearthe links, actuators, which resultingconverge in to a a workspacesingle point larger of the than ankle similar platform. parallel A special manipulators, joint design as ensures well as the human-like point convergence mobility, whichof the isthree also linear characterized actuators, by resulting no singular in a conﬁgurations, workspace larger as discussed than similar in [ 20parallel,21]. With manipulators, reference toas Figureswell as6 human-likeand9b, the kinematicsmobility, which of each is legalso can characterized be expressed by as no singular configurations, as discussed in [20,21]. With reference to Figures 6 and 9b, the kinematics of each leg can be expressed as B0 = A0Ai + li (4) 𝑩𝟎 = 𝑨𝟎𝑨 +𝒍𝒊 (4) where Ai represents the position of the spherical joints on the upper platform, A0 is the center of the where Ai represents the position of the spherical joints on the upper platform, A0 is the center of the upper platform, B0 is the point of convergence of the three limbs and the motion parameters are given upper platform, B0 is the point of convergence of the three limbs and the motion parameters are given by linear actuator lengths li. This formulation can be obtained from Equation (1) by imposing the by linear actuator lengths li. This formulation can be obtained from Equation (1) by imposing the convergence of the limbs and removing the ﬁxed-length central limb, and it can be used to control the convergence of the limbs and removing the fixed-length central limb, and it can be used to control motion of the locomotion system of the robot, as explained with details in [19–21]. the motion of the locomotion system of the robot, as explained with details in [19–21].

(a) (b) (c)

FigureFigure 9. 9.Leg Leg structure: structure: (a(a)) humanhuman legleg with with muscles; muscles; (b(b)) a a scheme scheme for for leg leg design; design; ( c()c) LARMbot LARMbot leg leg locomotorlocomotor prototype. prototype.

4.1. Experimental Validation Laboratory tests have been worked out to check the feasibility of the proposed design and to characterize the performance of the LARMbot prototype during its development. In particular, in this paper, experiences of lab testing are reported for motion analysis of the LARMbot leg—locomotor as a parallel biped. Figure 10 shows the structure of the tested LARMbot biped locomotor and a conceptual scheme for the control and test acquisition of biped walking. In Figure 10a, the location of the three sensors that are used for the acquisitions is shown, as well as the orientation of the two IMU (inertial measurement unit) sensors (1) and (2). In Figure 10b, a conceptual scheme is presented for the overall testing frame and connections. The ﬁrst IMU, denoted as (1), is attached to the left foot, and the second IMU, denoted as (2), is placed on the hip platform. A current sensor (CS) is denoted as (3), and it is ﬁxed on the hip platform where also the rest of the electronic components is installed. The control system is based on an Arduino Mega board to command the eight leg motors, where six of them are linear actuators, and two are rotational motors to drive the ankle joint of each leg. IMU (1) is attached to the left foot to characterize the walking operation cycle’s motion in terms of angular velocities and linear acceleration; IMU (2) is used to characterize the hip platform motion; and the current sensor is used to measure the power consumption during walking. An ESP8266-based board is Robotics 2020, 9, x 11 of 17

4.1. Experimental Validation Laboratory tests have been worked out to check the feasibility of the proposed design and to characterize the performance of the LARMbot prototype during its development. In particular, in this paper, experiences of lab testing are reported for motion analysis of the LARMbot leg—locomotor as a parallel biped. Figure 10 shows the structure of the tested LARMbot biped locomotor and a conceptual scheme for the control and test acquisition of biped walking. In Figure 10a, the location of the three sensors that are used for the acquisitions is shown, as well as the orientation of the two IMU (inertial measurement unit) sensors (1) and (2). In Figure 10b, a conceptual scheme is presented for the overall testing frame and connections. The first IMU, denoted as (1), is attached to the left foot, and the second IMU, denoted as (2), is placed on the hip platform. A current sensor (CS) is denoted as (3), and it is fixed on the hip platform where also the rest of the electronic components is installed. The control system is based on an Arduino Mega board to command the eight leg motors, where six of them are linear actuators, and two are rotational motors to drive the ankle joint of each leg. IMU (1)Robotics is attached2020, 9, 75to the left foot to characterize the walking operation cycle’s motion in terms of angular11 of 16 velocities and linear acceleration; IMU (2) is used to characterize the hip platform motion; and the current sensor is used to measure the power consumption during walking. An ESP8266-based board used to acquire and elaborate data from sensors. The information is sent wirelessly to a PC to store is used to acquire and elaborate data from sensors. The information is sent wirelessly to a PC to store data by using Wi-Fi. data by using Wi-Fi.

(a) (b)

FigureFigure 10. 10. AA laboratory laboratory setup setup at at LARM2 LARM2 in in Rome: Rome: (a ()a )Parallel Parallel biped biped and and sensors: sensors: (1) (1) inertial inertial measurementmeasurement unit unit (IMU) (IMU) at at the the foot, foot, (2) (2) IMU IMU at at the the hip, hip, (3) (3) current current sensor; sensor; (b (b) )a aconceptual conceptual scheme scheme of of thethe system. system.

TheThe walking walking cycle cycle was was defined defined by by programming programming th thee motion motion of of the the biped biped from from point point to to point. point. FiveFive different different points points are are stored, stored, which which include include the thecorresponding corresponding positions positions of the of linear the linear actuators actuators and theand rotations the rotations of the of ankle the ankle motors. motors. The Thefirst first point point describes describes the the statically statically balanced balanced position position at at the the beginningbeginning and and end of eacheach motionmotion cycle, cycle, while while the th othere other four four points points define define the the main main poses poses of the of robot the robotduring during each each step cycle.step cycle. Thus, Thus, the gaitthe gait is computed is computed by deriving by deriving the intermediatethe intermediate positions positions of the of the legs legsthrough through a zero-moment-point a zero-moment-point approach. approach. Four Four snapshots snapshots of of a walkinga walking operation operation test test are are shown shown in inFigure Figure 11 ,11, where where the the locomotor locomotor can becan observed be observ whileed while moving moving from afrom right-forward a right-forward double double support supportphase to phase a right to swing,a right passingswing, passing through through left swing left andswing left-forward and left-forward double double support support phase. phase. In this Inmotion, this motion, the three the linear three actuators linear actuators of each leg of contract each leg and contract extend withand extend a behavior with that a behavior corresponds that to correspondsthe muscles to of the the muscles human upperof the leg,huma asn discussed upper leg, previously. as discussed previously. Robotics 2020, 9, x 12 of 17

Figure 11. A snapshot of a walking test at LARM2 in Rome. Figure 11. A snapshot of a walking test at LARM2 in Rome.

The accelerationacceleration ofof thethe hiphip during during this this motion motion has has been been acquired acquired by by IMU IMU (2) (2) and and it isit reportedis reported in Figurein Figure 12. 12. The The main main motion motion takes takes place place along along the x -axisthe x-axis on the on horizontal the horizontal pavement pavement surface surface and can and be observedcan be observed in the continuous in the continuous periodic behavior periodic in behavior the graph, in which the graph, corresponds which to corresponds the back-and-forth to the motionback-and-forth of the hip motion during of human-like the hip du walking.ring human-like The y component walking. The of the y component acceleration of is insteadthe acceleration associated is instead associated to the lateral balancing motion of the hip, while the acceleration along the z-axis is negligible as referring to vertical displacements during a smooth walking.

-1 Acceleration [m/s2] -2 0 1000 2000 3000 4000 5000 6000 7000 Time [ms]

a_x [m/s2] a_y [m/s2] a_z [m/s2]

Figure 12. Acquired results of hip motion during a walking test in Figure 11 in terms of acceleration of the hip platform.

The acquisition data of IMU (1) are shown in Figure 13 and illustrate the behavior of the foot during the experimented walking gait. The main component is again in the x direction, with negative peaks corresponding to the foot’s dorsiflexion. When the foot is on the ground, the acceleration is negligible, as expected, although some vibration and slipping can be still observed in the data plot. The acquired data for the walking gait test in Figures 12 and 13 show a smooth motion, with acceleration values that are always smaller than 1.5 m/s2 in absolute value. Another significant characteristic of the LARMbot humanoid is its low power consumption. An estimation of the power consumption during the walking gait in Figure 11 can be obtained by the current sensor (3) acquisition together with the power supply voltage (7.4 V), and the results are reported in Figure 14. The static power draw is less than 4.00 W, with a peak of 8.09 W and an RMS (root main square) value is of 5.82 W during the walking operation. Large values of acceleration, up to 4.0 m/s2 in absolute value, can be observed instead in the squatting weight-lifting test that was reported in [17], with a 1.00 kg payload and results in Figure 15. The higher value is required by a needed faster balancing action, but the motion is still smooth, and the peak value is well within human-like motion. This acquisition refers to a test of squatting motion with a payload on the arms

Robotics 2020, 9, x 12 of 17

Figure 11. A snapshot of a walking test at LARM2 in Rome.

The acceleration of the hip during this motion has been acquired by IMU (2) and it is reported Roboticsin Figure2020 12., 9, 75The main motion takes place along the x-axis on the horizontal pavement surface12 ofand 16 can be observed in the continuous periodic behavior in the graph, which corresponds to the back-and-forth motion of the hip during human-like walking. The y component of the acceleration is to the lateral balancing motion of the hip, while the acceleration along the z-axis is negligible as instead associated to the lateral balancing motion of the hip, while the acceleration along the z-axis is referring to vertical displacements during a smooth walking. negligible as referring to vertical displacements during a smooth walking.

-1 Acceleration [m/s2] -2 0 1000 2000 3000 4000 5000 6000 7000 Time [ms]

a_x [m/s2] a_y [m/s2] a_z [m/s2]

Figure 12. Acquired results of hip motion during a walking test in Figure 11 in terms of acceleration Figure 12. Acquired results of hip motion during a walking test in Figure 11 in terms of acceleration of of the hip platform. the hip platform.

RoboticsThe 2020 acquisition, 9, x data of IMU (1) are shown in Figure 13 and illustrate the behavior of the13 footof 17 during the experimented walking gait. The main component is again in the x direction, with negative of the prototype, to show the feasibility and convenience of the parallel mechanisms in LARMbot peaks corresponding to the foot’s dorsiﬂexion.dorsiflexion. When When the the foot is on the ground, the acceleration is prototype in a typical high-load task, with the leg design working in coordination with the trunk for negligible, as expected, although some vibration and and slipping slipping can can be be still still observed observed in in the the data data plot. plot. balancing. The squatting motion consisted in a vertical up-down displacement of 40 mm at a speed The acquiredacquired data data for for the the walking walking gait testgait intest Figures in Figures 12 and 1312 show and a13 smooth show motion,a smooth with motion, acceleration with of 10 mm/s, which was obtained by an up-down displacement2 in the parallel legs that has been valuesacceleration that are values always that smaller are always than smaller 1.5 m/s2 thanin absolute 1.5 m/s value. in absolute value. properlyAnother balanced significant by the characteristic trunk motion of with the onLARMbotly a pitch humanoid adjustment, is its as low shown power in Figure consumption. 16. An estimation of the power consumption during the walking gait in Figure 11 can be obtained by the current sensor1.5 (3) acquisition together with the power supply voltage (7.4 V), and the results are reported in Figure 14. The static power draw is less than 4.00 W, with a peak of 8.09 W and an RMS 1 (root main square) value is of 5.82 W during the walking operation. Large values of acceleration, up to 4.0 m/s2 in0.5 absolute value, can be observed instead in the squatting weight-lifting test that was reported in [17], with a 1.00 kg payload and results in Figure 15. The higher value is required by a 0 needed faster balancing action, but the motion is still smooth, and the peak value is well within human-like-0.5 motion. This acquisition refers to a test of squatting motion with a payload on the arms Acceleration [m/s2] -1 0 1000 2000 3000 4000 5000 6000 7000 Time [ms]

a_x [m/s2] a_y [m/s2] a_z [m/s2]

Figure 13. Acquired results of foot motion during a walking test in Figure 11 in terms of acceleration Figure 13. Acquired results of foot motion during a walking test in Figure 11 in terms of acceleration of of the foot. the foot.

Another10 signiﬁcant characteristic of the LARMbot humanoid is its low power consumption. An estimation8 of the power consumption during the walking gait in Figure 11 can be obtained by the current sensor (3) acquisition together with the power supply voltage (7.4 V), and the results are 6 reported in Figure 14. The static power draw is less than 4.00 W, with a peak of 8.09 W and an RMS (root main square)4 value is of 5.82 W during the walking operation. Large values of acceleration, Power [W] 2 0 0 1000 2000 3000 4000 5000 6000 7000 Time [ms]

Figure 14. Acquired results of power consumption during a walking test as in Figure 11.

1 0 -1 -2 -3 -4 Acceleration [m/s2] -5 0 2000 4000 6000 8000 10000 12000 Time [ms]

a_x [m/s2] a_y [m/s2] a_z [m/s2]

Figure 15. Acquired results of trunk motion during a squat weight-lifting test with a 1.00 kg payload in terms of acceleration at the shoulders [17].

Robotics 2020, 9, x 13 of 17 Robotics 2020, 9, x 13 of 17 of the prototype, to show the feasibility and convenience of the parallel mechanisms in LARMbot of the prototype, to show the feasibility and convenience of the parallel mechanisms in LARMbot prototype in a typical high-load task, with the leg design working in coordination with the trunk for prototype in a typical high-load task, with the leg design working in coordination with the trunk for balancing. The squatting motion consisted in a vertical up-down displacement of 40 mm at a speed balancing. The squatting motion consisted in a vertical up-down displacement of 40 mm at a speed of 10 mm/s, which was obtained by an up-down displacement in the parallel legs that has been of 10 mm/s, which was obtained by an up-down displacement in the parallel legs that has been properly balanced by the trunk motion with only a pitch adjustment, as shown in Figure 16. properly balanced by the trunk motion with only a pitch adjustment, as shown in Figure 16.

1.5 1.5 1 1 0.5 0.5 Robotics 2020, 9, 75 13 of 16 0 0 -0.52 up to 4.0 mAcceleration [m/s2] /-0.5s in absolute value, can be observed instead in the squatting weight-lifting test that was reported inAcceleration [m/s2] [-117], with a 1.00 kg payload and results in Figure 15. The higher value is required by -1 a needed faster balancing0 1000 action, but 2000 the motion 3000 is still smooth,4000 and 5000 the peak 6000 value is well7000 within 0 1000 2000 3000 4000 5000 6000 7000 human-like motion. This acquisition refers to a testTime of [ms] squatting motion with a payload on the arms of the prototype, to show the feasibility and convenienceTime [ms] of the parallel mechanisms in LARMbot prototype in a typical high-load task, with the leg design working in coordination with the trunk for a_x [m/s2] a_y [m/s2] a_z [m/s2] balancing. The squatting motiona_x consisted [m/s2] in a verticala_y [m/s2] up-down displacementa_z [m/s2] of 40 mm at a speed of 10 mm/s, which was obtained by an up-down displacement in the parallel legs that has been properly Figure 13. Acquired results of foot motion during a walking test in Figure 11 in terms of acceleration balancedFigure by 13. the Acquired trunk motion results of with foot only motion a pitch during adjustment, a walking test as shownin Figure in 11 Figure in terms 16. of acceleration of the foot. of the foot.

10 10 8 8 6 6 4 4 Power [W] 2 Power [W] 2 0 0 0 1000 2000 3000 4000 5000 6000 7000 0 1000 2000 3000 4000 5000 6000 7000 Time [ms] Time [ms]

Figure 14. Acquired results of power consumption during a walking test as in Figure 11. Figure 14. Acquired results of power consumption during a walking test as in Figure 1111..

1 1 0 0 -1 -1 -2 -2 -3 -3 -4

Acceleration [m/s2] -4

Acceleration [m/s2] -5 -5 0 2000 4000 6000 8000 10000 12000 0 2000 4000 6000 8000 10000 12000 Time [ms] Time [ms]

a_x [m/s2] a_y [m/s2] a_z [m/s2] a_x [m/s2] a_y [m/s2] a_z [m/s2]

Figure 15. Acquired results of trunk motion during a squat weight-lifting test with a 1.00 kg payload Figure 15. Acquired results of trunk motion during a squat weight-lifting test with a 1.00 kg payload Figurein terms 15. ofAcquired acceleration results at the of trunkshoulders motion [17]. during a squat weight-lifting test with a 1.00 kg payload in in terms of acceleration at the shoulders [17]. terms of acceleration at the shoulders [17].

Summarizing the design peculiarities and the laboratory experiences, the parallel mechanisms with human anatomy inspiration in the LARMbot design provide a signiﬁcant high performance in payload and energy eﬃciency, as well as the required motion capability for basic humanoid operations. Robotics 2020, 9, 75 14 of 16

Robotics 2020, 9, x 14 of 17

25 20 15 10 5 0 -5

Angular displacement Angular displacement [deg] 0 2000 4000 6000 8000 10000 12000 Time [ms]

Pitch [°] Roll [°] Yaw [°]

Figure 16. Acquired results of trunk motion during a squat weight-lifting test with a 1.00 kg payload Figure 16. Acquired results of trunk motion during a squat weight-lifting test with a 1.00 kg payload in in terms of angular displacement at the shoulders [17]. terms of angular displacement at the shoulders [17].

4.2. ComparisonSummarizing with the Serial design Architectures peculiarities and the laboratory experiences, the parallel mechanisms with human anatomy inspiration in the LARMbot design provide a significant high performance in payload In order to outline the advantages of parallel mechanisms over serial architectures, a comparison and energy efficiency, as well as the required motion capability for basic humanoid operations. between the LARMbot humanoid and the successful NAO design is here reported. The data for LARMbot is obtained either from the experiments presented in Section4 or from previous works [ 17,31], 4.2. Comparison with Serial Architectures whereas the technical specifications of the NAO humanoid can be found on the website of its manufacturer,In order to Aldebaran outline the Roboticsadvantages [32 of]. parallel The performance mechanisms values over serial of both architectures, LARMbot and a comparison NAO are summarizedbetween the inLARMbot Table3, with humanoid reference and to the requirementssuccessful NAO of Table design2. is here reported. The data for LARMbot is obtained either from the experiments presented in Section 4 or from previous works [17,31], whereas the technicalTable 3. specificationsLARMbot performance of the NAO characteristics humanoid [16 can–19 be,31 ,found32]. on the website of its manufacturer, Aldebaran Robotics [32]. The performance values of both LARMbot and NAO are Characteristics LARMbot NAO V5 summarized in Table 3, with reference to the requirements of Table 2. Height 0.85 m 0.57 m Weight 3.70 kg 5.5 kg Table 3. LARMbot performance characteristics [16–19,31,32]. Step length (natural) 100% leg height 50% leg height StepCharacteristics length (fast) LARMbot 100% leg height NAO 50% V5 leg height Speed 100 steps per minute 120 steps per minute Height 0.85 m 0.57 m Leg mobility 5 D.o.F. 5 D.o.F. Leg payloadWeight capacity 180%3.70 kg body weight 5.5 kg - StepArm length mobility (natural) 100% leg 6height D.o.F. 50% leg height 5 D.o.F. ArmStep payload length capacity (fast) 100% 20% leg bodyheight weight 50% leg 0.03% height body weight TorsoSpeed mobility 100 steps per 3 D.o.F.minute 120 steps per 1minute D.o.F. Torso flexion/extension 0–45 0 Leg mobility 5 D.o.F. ◦ 5 D.o.F. Torso lateral bending 0–45◦ 0 PowerLeg payload consumption capacity 180% body 7.00 weight W/kg Battery: - 60 min of active use Arm mobility 6 D.o.F. 5 D.o.F. Arm payload capacity 20% body weight 0.03% body weight Even though NAO is able to maintain a faster step rate than the LARMbot, it is outperformed by Torso mobility 3 D.o.F. 1 D.o.F. the latter in payload and efficiency. The parallel architectures of the LARMbot enable a much higher Torso flexion/extension 0–45° 0 payload and payload to weight ratio, while still maintaining a lightweight design. Usually, serial Torso lateral bending 0–45° 0 architectures are preferred to parallel ones for their improved workspace and reach. However, in this Power consumption 7.00 W/kg Battery: 60 min of active use case, thanks to its properly designed human-inspired parallel mechanisms, the LARMbot design shows a good performance, not only in payload and energy consumption, but also in workspace, mobility Even though NAO is able to maintain a faster step rate than the LARMbot, it is outperformed and speed, which can be considered comparable to human ones. The main drawback of parallel design by the latter in payload and efficiency. The parallel architectures of the LARMbot enable a much is given by singular configurations and increased control complexity (e.g., kinematics that cannot be higher payload and payload to weight ratio, while still maintaining a lightweight design. Usually, solved in closed form or with multiple solutions, force closure for cable-driven mechanisms). serial architectures are preferred to parallel ones for their improved workspace and reach. However, in this case, thanks to its properly designed human-inspired parallel mechanisms, the LARMbot

Robotics 2020, 9, 75 15 of 16

A comparison with NAO only is here reported, since it has a similar size of LARMbot and comparable characteristics. Some other examples may include the iCub [5] and ASIMO [2] platforms that are of a different (larger) size. In general, it can be concluded that parallel mechanisms with antagonist functioning give improved mechanical performance of the humanoid operation in terms of accuracy, stiffness, payload and efficiency, at the not particularly high expense of control complexity.

5. Conclusions This paper described how parallel mechanisms can be used in humanoid robots in order to improve their structure and operation performance as inspired by human anatomy. Any complex of bones and antagonist muscles in the human body can be modelled as a parallel mechanism whose design can be used for the architecture of humanoid robots. The concept is presented by analyzing the main parts of the human body and extracting a corresponding humanoid robot design with parallel mechanisms, and by discussing requirements and peculiarities for humanoid structures and operations. An illustrative example is reported from the authors’ experience with the LARMbot design to show a successful design and implementation of parallel mechanisms in a humanoid robot. The LARMbot design is based on parallel mechanisms to achieve an eﬃcient compact humanoid design with enhanced performance by replicating concepts from human anatomy.

Author Contributions: Conceptualization, M.C.; methodology, M.C.; software, M.R.; experiments, M.R. and C.M.-C.; data curation, M.R.; writing—original draft preparation, M.C. and M.R.; writing—review and editing, M.C.; supervision, M.C. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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