IROS2019国际学术会议论文集 1375

Common Dimensional Autoencoder for Learning Redundant Muscle Posture Mappings of Complex Musculoskeletal Robots Hiroaki Masuda1 Arne Hitzmann1 Koh Hosoda1and Shuhei Ikemoto1 Abstract It has been widely considered that a distinctive feature of musculoskeletal structures is that both the joint angle and stiffness can be changed by exploiting the agonist antagonist driving of the joint However musculoskeletal sys tems in animals and humans are typically highly complex and the simple agonist antagonist driving is rarely found Therefore in accordance with the increasing complexity of musculoskeletal robots the feature that causes the robot to assume a posture with different stiffness values becomes diffi cult to achieve owing to the diffi culty in modeling the kinematics Although data driven approaches such as the neural network are regarded as suitable for modeling complex relationships the training data are diffi cult to obtain because measuring joint stiffness is typically extremely diffi cult in contrast to measuring an actuator s state and posture Hence we herein propose the common dimensional autoencoder where the encoded feature exhibits identical dimensions to the original input vector In the proposed network in parallel with the original unsupervised training using the data of the actuators states supervised training at part of the encoded features is performed using posture data Consequently features expressing the redundancy of inverse kinematics appear at the remaining part of the encoded features without using data such as joint stiffness The validity of the proposed method was confi rmed successfully through an experiment using a 10 degrees of freedom complex musculoskeletal robot arm driven by pneumatic artifi cial mus cles I INTRODUCTION Living organisms can behave adaptively in complex en vironments by skillfully manipulating their complex bodies It has been regarded that their distinctive body structures namely musculoskeletal structures contribute signifi cantly in achieving adaptive behavior Therefore many musculoskele tal robots have been experimentally developed in bioinspired robotics to clarify and exploit functionalities provided by musculoskeletal systems 1 2 3 4 5 A well known functionality of musculoskeletal systems is the control of both the angle and stiffness of a joint In contrast with joints that are typically driven by a sin gle rotatory actuator in conventional robots if a joint is driven through tendons by two agonist antagonist pairs of springy actuators the redundancy in the drive system can be used to change the stiffness 6 7 Thus far this property has been studied intensively in tendon driven systems It is well known that musculoskeletal systems with actuators driving both single and multiple joints i e actuators cor responding to multiarticular muscles are still suffi ciently This work was supported by JSPS KAKENHI Grant Number 18H01410 1The authors are with Graduate School of Life Science and Systems Engineering Kyushu Institute of Technology 2 4 Hibikino Wakamatsu ku Kitakyushu 808 0196 Japan ikemoto brain kyutech ac jp Fig 1 Example of redundancy in a complex musculoskeletal robot The same hand position can be achieved in different postures with different actuator states This robot has a three dimensional complex musculoskeletal structure driven by pneumatic artifi cial muscles Different sets of internal pressures of pneumatic artifi cial muscles exist while the same hand position remains modeled and controlled if agonist antagonist pairs can be analytically identifi ed 8 9 10 However because the musculoskeletal systems of animals and humans are highly complex to identify agonist antagonist pairs of muscles in advance musculoskeletal robots have been developed with increased structural complexity Further several complex musculoskeletal robots have been developed such that the conventional analytic approach can be disregarded 11 12 13 Data driven methods such as frameworks using the neural network NN will be a promising candidate to overcome the diffi culty in modeling a complex musculoskeletal struc ture For instance Jantsch et al approximated the muscle Jacobian of a spherical joint using a multilayered percep tron network 14 Further Jamone et al modeled a muscle Jacobian by adopting a receptive fi eld NN for their tendon driven neck structure inspired by the structure of humans 15 However in these studies the feature of a musculoskeletal system that varies in stiffness has been neither approximated nor exploited Because an NN typically provides individ ual mapping redundancy that appears in mapping from a posture to an actuator state must be handled explicitly by preparing training data that fully explain the difference in the same posture realized by different actuator states It is evident that preparing this type of data is more diffi cult than preparing the data of actuator states and postures Hence Okubo et al adopted a functional approximation of forwarding kinematics and solved the redundant inverse kinematics problem numerically based on the differentiation 2019 IEEE RSJ International Conference on Intelligent Robots and Systems IROS Macau China November 4 8 2019 978 1 7281 4003 2 19 31 00 2019 IEEE2545 of forward mapping 16 Although they proposed a method of bidirectional mapping for redundant kinematics problems exploiting the redundancy e g varying the actuator state while maintaining the same posture is required for the numerical method which can be time consuming compared with approaches using the NN If training an NN to express both forward and inverse mappings between the actuator states and postures becomes available only based on easily obtainable data while redundancy provided by different stiffnesses and redundant joints for the task accomplishment is stored simultaneously a viable alternative can be achieved In this study we propose a new NN based method for highly redundant kinematics problems found in complex musculoskeletal robots Because measuring the stiffness of all joints is typically diffi cult the proposed method is re quired to train the NN without relying on this type of data Further because even measuring angles of all joints in musculoskeletal robots is often diffi cult e g measuring three angles of a spherical joint it must be deemed as redundant if it is not considered explicitly in the task accomplishment Fig 1 shows an example of this problem that appears in our musculoskeletal robot arm In the pro posed method unsupervised and supervised learning were performed simultaneously to create both forward and inverse mappings of the kinematics Briefl y this method directly trains a part of feature units in a general autoencoder in the supervised learning manner during the original unsupervised learning such that the remaining of the feature units obtain the information that is not contained in the supervised data but required to accomplish unsupervised learning i e redundant information such as joint stiffness Thus far we have verifi ed the core idea through a simulation of a 2 degrees of freedom DOF planar manipulator driven by a typical 3 pairs 6 muscles confi guration 17 However it has not been evaluated whether the proposed method can be applied to complex musculoskeletal robots that require data driven approaches Therefore in this study we conducted an experiment using a 10 DOF complex musculoskeletal robot arm driven by pneumatic artifi cial muscles The experiment validated the method II PROPOSED METHOD In this section we explain the proposed method using a general setup where a mapping from high dimensional data DHto low dimensional data DLis a many to one mapping For instance u DH RNand q DL RM where M N holds can be assumed to correspond to the actuator states and postures respectively Fig 2 shows the network used in the proposed method The proposed method consists of the unsupervised and supervised learning of the NN The unsu pervised learning aims to transform high dimensional data to feature vectors and back again Therefore it is precisely the same as a general autoencoder Meanwhile the supervised learning aims to force a part of the feature vector i e M dimensional subvector out of N dimensional vector to mean corresponding to low dimensional data It indicates that the forward mapping from the high dimensional data to the low Fig 2 The network used in the proposed method is a simple autoencoder trained by feeding high dimensional data DHto both the input and output units depicted as black circles Because the bottleneck hidden layer where low dimensional feature vectors are typically expressed exhibits the identi cal dimensionality with the input and output layers we name this network the typical dimensional autoencoder Simultaneously supervised learning is performed by feeding low dimensional data DLto part of the feature units on the bottleneck layer depicted as dark gray circles dimensional data is trained explicitly in the subnetwork of the autoencoder It is noteworthy that the unsupervised and supervised training are performed simultaneously In this case the remaining feature vectors must retain information that is not contained in the low dimensional data but required to reproduce high dimensional data In other words it has to exhibit vectors that distinguish many input vectors of the many to one forward mapping The important feature of the proposed method is that the remaining part is not trained explicitly but implicitly guided to express such information meaning the redundancy in the inverse mapping Once the training is suffi ciently accomplished a variety of high dimensional vectors that realizes the same low dimensional vector can be obtained by fi xing the trained part of the feature units i e dark gray circles in Fig 2 to the low dimensional vector and by varying the remaining i e light gray circles in Fig 2 See Fig 3 for more details As shown in Fig 2 the bottleneck layer of the autoencoder exhibits identical dimensionality to the input and output and is named the common dimensional autoencoder This is because the dimensionality required for expressing the redundancy does not exceed N M and N units common to the input and output of the autoencoder are required for the feature vector at the maximum It is noteworthy that the other hidden layers contain more than N units The unsupervised learning was performed by referring to the following cost function LAE 1 kDHk ui DN y ui ui TQ y ui ui 1 where y ui indicates the output of the common dimensional autoencoder obtained by feeding uito the input layer and by transforming back through the bottleneck hidden layer In addition Q indicates a weighting matrix This is the general form of the cost function of the autoencoder The supervised learning was only performed in the sub network of the common dimensional autoencoder Let us denote vectors that appear on the bottleneck hidden layer as h Assuming a column vector hT I RMas the subvector of h where hT I hTK T h holds the cost function for the supervised learning is written as follows 2546 Fig 3 Functions of subnetworks achieved in the typical dimensional autoencoder The network is sandwiched between the input layer and the bottleneck hidden layer where units received DL upper left are trained explicitly to be the forward mapping Meanwhile the remaining half of the encoder lower left is not trained explicitly but implicitly guided such that the remaining information is lost in the forward mapping as a result of training the entire autoencoder Once the training is successful it is obvious that the decoder right can be used for inverse mapping In particular a variety of high dimensional vectors that induce the same low dimensional data can be obtained by feeding the low dimensional vector to units depicted in dark gray upper right and by feeding a variety of adequate vectors to units depicted in light gray lower left LFM 1 kDLk ui qi DH DL hI ui qi TR hI ui qi 2 where R and hI ui indicate a weighting matrix and a vector that appear at hIwhen uiis fed onto the input layer respectively This is the general cost function of the simple feedforward NN and governs the training of the forward mapping The entire cost function for the common dimensional autoencoder is defi ned as L LAE LFM 3 In the training we did not assume any restriction of tech niques regarding the activation functions optimization tech nique etc Additionally even for the network structures of the encoder and decoder the proposed method allows for the use of any confi guration except for shortcut connections beyond the bottleneck layer As shown above the remaining units on the bottleneck hidden layer hKis not trained explicitly However qualita tively hKis required to possess information that has been lost by the many to one forward mapping from DHto DLbecause the entire network has to reproduce DHon the output layer eventually From the analogy of linear algebra hIand hKare regarded as the image and kernel of the function f u q respectively The kernel null space is typically employed to explain how the joint stiffness and other variables appear as redundant in the kinematics models of the tasks and the common dimensional autoencoder introduces the same viewpoint to complex musculoskeletal robots Fig 4 Muscle arrangements of the musculoskeletal robot arm and a human This robot arm has a 10 DOF skeletal structure where the scapula shoulder joint elbow joint forearm and wrist have 3 DOFs 3 DOFs 1 DOF 1 DOF and 2 DOFs respectively All joints are driven redundantly by 24 PAMs arranged similarly to the corresponding human muscles Each PAM has a pressure sensor SMC PSE 540 and the internal pressure is controlled by an air fl ow control valve Festo MPYE 5 A yellow ball is attached instead of the hand and the Cartesian position is tracked using a depth camera Intel RealSense ZR 300 The origin is located at the base of the upper torso A visualization of the robot s coordinate system s origin is also referenced in the image above III EXPERIMENT In this section we verify the proposed method using the 10 DOF musculoskeletal robot arm 18 Fig 4 shows the musculoskeletal structure of the robot arm In this robot arm 24 pneumatic artifi cial muscles PAMs corresponding to the muscle arrangement of humans are employed Further the Cartesian position of the hand where the yellow ball is at tached is measured using a depth camera In the experiment we focused on the bidirectional mapping between the internal pressures of all PAMs and their resulting hand positions In other words in this experiment the actuator state and the posture in the previous section correspond specifi cally to the internal pressures of the PAMs and the Cartesian position of the hand Therefore N 24 and M 3 hold in this problem It is clear that the forward mapping that transforms the internal pressures to the corresponding hand position is a many to one mapping and redundancy appears in the inverse mapping In the following subsections fi rst the procedure to gather training data DHand DLis explained in detail Further the structure and training of the common dimensional au 2547 toencoder employed in this setup are explained The second subsection presents the result and discussion of control based on the trained common dimensional autoencoder A Training of the Common Dimensional Autoencoder To train the common dimensional autoencoder DHand DLare collected by moving the musculoskeletal robot arm A data point in DHindicates a vector consisting of the internal pressures of the PAMs To sample the data points the pressure of each PAM was selected randomly between 0 and 0 5 MPa with an interval of 0 01 The corresponding data point in DLindicating the hand position was measured when the musculoskeletal robot arm reached equilibrium at the given pressures By executing this procedure repeatedly 1 million points of DHand DLwere gathered from the musculoskeletal robot arm Based on DHand DL the training of the common dimen sional autoencoder was performed Regarding the network structure because 24 actuators were used in this experiment 24 units were used on the input layer bottleneck hidden layer and output layer Three hidden layers exist between the input layer and bottleneck hidden layer as well as between the bottleneck hidden layer and output layer For these hidden layers 180 120 and 60 units were employed between the input and bottleneck layers and in the reverse order between the bottleneck and output layer Each layer except the output layer has an additional bias unit that always outputs 1 Because the hand position is expressed in the form of a three dimensional vector 3 out of 24 units on the bottleneck hidden layer are trained explicitly to output the corresponding data points in DL For the training the Adam optimization algorithm was used and the entire cost value was reduced suffi ciently B Posture control based on inverse mapping To verify whether the common dimensional autoencoder had learned the bidirectional mapping between the PAM pressures and hand positions we conducted a hand position control experiment using the musculoskeletal robot arm For the experiment the desired hand positions were generated as follows h I x y z 0 15cos 0 05 0 15sin 0 30 0 27 4 where varies from 0 to 2 with the interval 10 Thus 20 desired hand positions exist on a circular path on a horizontal plane The hI which three units trained by referring the DL receives individually from these 20 desired hand positions in the decoder part of the common dimensional autoencoder The right half of the network See Fig 3 If the proposed method operates as expected and the training was performed suffi ciently although the hK i e the remaining units on the bottleneck hidden layer affects the values on the output layer the same hand position will be achieved using these values as the desired internal pressures of the PAMs Therefore we can randomly generate values of 21 units contained in hKwithin the ran