Biomimetic Manipulator Control Design for Bimanual Tasks in the Natural Environment

As robots become more prolific in the human environment, it is important that safe operational procedures are introduced at the same time; typical robot control methods are often very stiff to maintain good positional tracking, but this makes contact (purposeful or accidental) with the robot dangerous. In addition, if robots are to work cooperatively with humans, natural interaction between agents will make tasks easier to perform with less effort and learning time. Stability of the robot is particularly important in this situation, especially as outside forces are likely to affect the manipulator when in a close working environment; for example, a user leaning on the arm, or task-related disturbance at the end-effector. Recent research has discovered the mechanisms of how humans adapt the applied force and impedance during tasks. Studies have been performed to apply this adaptation to robots, with promising results showing an improvement in tracking and effort reduction over other adaptive methods. The basic algorithm is straightforward to implement, and allows the robot to be compliant most of the time and only stiff when required by the task. This allows the robot to work in an environment close to humans, but also suggests that it could create a natural work interaction with a human. In addition, no force sensor is needed, which means the algorithm can be implemented on almost any robot. This work develops a stable control method for bimanual robot tasks, which could also be applied to robot-human interactive tasks. A dynamic model of the Baxter robot is created and verified, which is then used for controller simulations. The biomimetic control algorithm forms the basis of the controller, which is developed into a hybrid control system to improve both task-space and joint-space control when the manipulator is disturbed in the natural environment. Fuzzy systems are implemented to remove the need for repetitive and time consuming parameter tuning, and also allows the controller to actively improve performance during the task. Experimental simulations are performed, and demonstrate how the hybrid task/joint-space controller performs better than either of the component parts under the same conditions. The fuzzy tuning method is then applied to the hybrid controller, which is shown to slightly improve performance as well as automating the gain tuning process. In summary, a novel biomimetic hybrid controller is presented, with a fuzzy mechanism to avoid the gain tuning process, finalised with a demonstration of task-suitability in a bimanual-type situation.EPSR

Human-Machine Interface for Remote Training of Robot Tasks

Regardless of their industrial or research application, the streamlining of robot operations is limited by the proximity of experienced users to the actual hardware. Be it massive open online robotics courses, crowd-sourcing of robot task training, or remote research on massive robot farms for machine learning, the need to create an apt remote Human-Machine Interface is quite prevalent. The paper at hand proposes a novel solution to the programming/training of remote robots employing an intuitive and accurate user-interface which offers all the benefits of working with real robots without imposing delays and inefficiency. The system includes: a vision-based 3D hand detection and gesture recognition subsystem, a simulated digital twin of a robot as visual feedback, and the "remote" robot learning/executing trajectories using dynamic motion primitives. Our results indicate that the system is a promising solution to the problem of remote training of robot tasks.Comment: Accepted in IEEE International Conference on Imaging Systems and Techniques - IST201

Robot Manipulators

Robot manipulators are developing more in the direction of industrial robots than of human workers. Recently, the applications of robot manipulators are spreading their focus, for example Da Vinci as a medical robot, ASIMO as a humanoid robot and so on. There are many research topics within the field of robot manipulators, e.g. motion planning, cooperation with a human, and fusion with external sensors like vision, haptic and force, etc. Moreover, these include both technical problems in the industry and theoretical problems in the academic fields. This book is a collection of papers presenting the latest research issues from around the world

Bimanual robot skills: MP encoding, dimensionality reduction and reinforcement learning

In our culture, robots have been in novels and cinema for a long time, but it has been specially in the last two decades when the improvements in hardware - better computational power and components - and advances in Artificial Intelligence (AI), have allowed robots to start sharing spaces with humans. Such situations require, aside from ethical considerations, robots to be able to move with both compliance and precision, and learn at different levels, such as perception, planning, and motion, being the latter the focus of this work. The first issue addressed in this thesis is inverse kinematics for redundant robot manipulators, i.e: positioning the robot joints so as to reach a certain end-effector pose. We opt for iterative solutions based on the inversion of the kinematic Jacobian of a robot, and propose to filter and limit the gains in the spectral domain, while also unifying such approach with a continuous, multipriority scheme. Such inverse kinematics method is then used to derive manipulability in the whole workspace of an antropomorphic arm, and the coordination of two arms is subsequently optimized by finding their best relative positioning. Having solved the kinematic issues, a robot learning within a human environment needs to move compliantly, with limited amount of force, in order not to harm any humans or cause any damage, while being as precise as possible. Therefore, we developed two dynamic models for the same redundant arm we had analysed kinematically: The first based on local models with Gaussian projections, and the second characterizing the most problematic term of the dynamics, namely friction. Such models allowed us to implement feed-forward controllers, where we can actively change the weights in the compliance-precision tradeoff. Moreover, we used such models to predict external forces acting on the robot, without the use of force sensors. Afterwards, we noticed that bimanual robots must coordinate their components (or limbs) and be able to adapt to new situations with ease. Over the last decade, a number of successful applications for learning robot motion tasks have been published. However, due to the complexity of a complete system including all the required elements, most of these applications involve only simple robots with a large number of high-end technology sensors, or consist of very simple and controlled tasks. Using our previous framework for kinematics and control, we relied on two types of movement primitives to encapsulate robot motion. Such movement primitives are very suitable for using reinforcement learning. In particular, we used direct policy search, which uses the motion parametrization as the policy itself. In order to improve the learning speed in real robot applications, we generalized a policy search algorithm to give some importance to samples yielding a bad result, and we paid special attention to the dimensionality of the motion parametrization. We reduced such dimensionality with linear methods, using the rewards obtained through motion repetition and execution. We tested such framework in a bimanual task performed by two antropomorphic arms, such as the folding of garments, showing how a reduced dimensionality can provide qualitative information about robot couplings and help to speed up the learning of tasks when robot motion executions are costly.A la nostra cultura, els robots han estat presents en novel·les i cinema des de fa dècades, però ha sigut especialment en les últimes dues quan les millores en hardware (millors capacitats de còmput) i els avenços en intel·ligència artificial han permès que els robots comencin a compartir espais amb els humans. Aquestes situacions requereixen, a banda de consideracions ètiques, que els robots siguin capaços de moure's tant amb suavitat com amb precisió, i d'aprendre a diferents nivells, com són la percepció, planificació i moviment, essent l'última el centre d'atenció d'aquest treball. El primer problema adreçat en aquesta tesi és la cinemàtica inversa, i.e.: posicionar les articulacions del robot de manera que l'efector final estigui en una certa posició i orientació. Hem estudiat el camp de les solucions iteratives, basades en la inversió del Jacobià cinemàtic d'un robot, i proposem un filtre que limita els guanys en el seu domini espectral, mentre també unifiquem tal mètode dins un esquema multi-prioritat i continu. Aquest mètode per a la cinemàtica inversa és usat a l'hora d'encapsular tota la informació sobre l'espai de treball d'un braç antropomòrfic, i les capacitats de coordinació entre dos braços són optimitzades, tot trobant la seva millor posició relativa en l'espai. Havent resolt les dificultats cinemàtiques, un robot que aprèn en un entorn humà necessita moure's amb suavitat exercint unes forces limitades per tal de no causar danys, mentre es mou amb la màxima precisió possible. Per tant, hem desenvolupat dos models dinàmics per al mateix braç robòtic redundant que havíem analitzat des del punt de vista cinemàtic: El primer basat en models locals amb projeccions de Gaussianes i el segon, caracteritzant el terme més problemàtic i difícil de representar de la dinàmica, la fricció. Aquests models ens van permetre utilitzar controladors coneguts com "feed-forward", on podem canviar activament els guanys buscant l'equilibri precisió-suavitat que més convingui. A més, hem usat aquests models per a inferir les forces externes actuant en el robot, sense la necessitat de sensors de força. Més endavant, ens hem adonat que els robots bimanuals han de coordinar els seus components (braços) i ser capaços d'adaptar-se a noves situacions amb facilitat. Al llarg de l'última dècada, diverses aplicacions per aprendre tasques motores robòtiques amb èxit han estat publicades. No obstant, degut a la complexitat d'un sistema complet que inclogui tots els elements necessaris, la majoria d'aquestes aplicacions consisteixen en robots més aviat simples amb costosos sensors d'última generació, o a resoldre tasques senzilles en un entorn molt controlat. Utilitzant el nostre treball en cinemàtica i control, ens hem basat en dos tipus de primitives de moviment per caracteritzar la motricitat robòtica. Aquestes primitives de moviment són molt adequades per usar aprenentatge per reforç. En particular, hem usat la búsqueda directa de la política, un camp de l'aprenentatge per reforç que usa la parametrització del moviment com la pròpia política. Per tal de millorar la velocitat d'aprenentatge en aplicacions amb robots reals, hem generalitzat un algoritme de búsqueda directa de política per a donar importància a les mostres amb mal resultat, i hem donat especial atenció a la reducció de dimensionalitat en la parametrització dels moviments. Hem reduït la dimensionalitat amb mètodes lineals, utilitzant les recompenses obtingudes EN executar els moviments. Aquests mètodes han estat provats en tasques bimanuals com són plegar roba, usant dos braços antropomòrfics. Els resultats mostren com la reducció de dimensionalitat pot aportar informació qualitativa d'una tasca, i al mateix temps ajuda a aprendre-la més ràpid quan les execucions amb robots reals són costoses

Bimanual robot skills: MP encoding, dimensionality reduction and reinforcement learning

Aplicat embargament des de la data de defensa fins 1/7/2018Premio a la mejor Tesis Doctoral sobre Robótica, Edición 2017, atorgat pel Comité Español de Automática.Finalista del 2018 George Girault PhD Award, from EuRoboticsIn our culture, robots have been in novels and cinema for a long time, but it has been specially in the last two decades when the improvements in hardware - better computational power and components - and advances in Artificial Intelligence (AI), have allowed robots to start sharing spaces with humans. Such situations require, aside from ethical considerations, robots to be able to move with both compliance and precision, and learn at different levels, such as perception, planning, and motion, being the latter the focus of this work. The first issue addressed in this thesis is inverse kinematics for redundant robot manipulators, i.e: positioning the robot joints so as to reach a certain end-effector pose. We opt for iterative solutions based on the inversion of the kinematic Jacobian of a robot, and propose to filter and limit the gains in the spectral domain, while also unifying such approach with a continuous, multipriority scheme. Such inverse kinematics method is then used to derive manipulability in the whole workspace of an antropomorphic arm, and the coordination of two arms is subsequently optimized by finding their best relative positioning. Having solved the kinematic issues, a robot learning within a human environment needs to move compliantly, with limited amount of force, in order not to harm any humans or cause any damage, while being as precise as possible. Therefore, we developed two dynamic models for the same redundant arm we had analysed kinematically: The first based on local models with Gaussian projections, and the second characterizing the most problematic term of the dynamics, namely friction. Such models allowed us to implement feed-forward controllers, where we can actively change the weights in the compliance-precision tradeoff. Moreover, we used such models to predict external forces acting on the robot, without the use of force sensors. Afterwards, we noticed that bimanual robots must coordinate their components (or limbs) and be able to adapt to new situations with ease. Over the last decade, a number of successful applications for learning robot motion tasks have been published. However, due to the complexity of a complete system including all the required elements, most of these applications involve only simple robots with a large number of high-end technology sensors, or consist of very simple and controlled tasks. Using our previous framework for kinematics and control, we relied on two types of movement primitives to encapsulate robot motion. Such movement primitives are very suitable for using reinforcement learning. In particular, we used direct policy search, which uses the motion parametrization as the policy itself. In order to improve the learning speed in real robot applications, we generalized a policy search algorithm to give some importance to samples yielding a bad result, and we paid special attention to the dimensionality of the motion parametrization. We reduced such dimensionality with linear methods, using the rewards obtained through motion repetition and execution. We tested such framework in a bimanual task performed by two antropomorphic arms, such as the folding of garments, showing how a reduced dimensionality can provide qualitative information about robot couplings and help to speed up the learning of tasks when robot motion executions are costly.A la nostra cultura, els robots han estat presents en novel·les i cinema des de fa dècades, però ha sigut especialment en les últimes dues quan les millores en hardware (millors capacitats de còmput) i els avenços en intel·ligència artificial han permès que els robots comencin a compartir espais amb els humans. Aquestes situacions requereixen, a banda de consideracions ètiques, que els robots siguin capaços de moure's tant amb suavitat com amb precisió, i d'aprendre a diferents nivells, com són la percepció, planificació i moviment, essent l'última el centre d'atenció d'aquest treball. El primer problema adreçat en aquesta tesi és la cinemàtica inversa, i.e.: posicionar les articulacions del robot de manera que l'efector final estigui en una certa posició i orientació. Hem estudiat el camp de les solucions iteratives, basades en la inversió del Jacobià cinemàtic d'un robot, i proposem un filtre que limita els guanys en el seu domini espectral, mentre també unifiquem tal mètode dins un esquema multi-prioritat i continu. Aquest mètode per a la cinemàtica inversa és usat a l'hora d'encapsular tota la informació sobre l'espai de treball d'un braç antropomòrfic, i les capacitats de coordinació entre dos braços són optimitzades, tot trobant la seva millor posició relativa en l'espai. Havent resolt les dificultats cinemàtiques, un robot que aprèn en un entorn humà necessita moure's amb suavitat exercint unes forces limitades per tal de no causar danys, mentre es mou amb la màxima precisió possible. Per tant, hem desenvolupat dos models dinàmics per al mateix braç robòtic redundant que havíem analitzat des del punt de vista cinemàtic: El primer basat en models locals amb projeccions de Gaussianes i el segon, caracteritzant el terme més problemàtic i difícil de representar de la dinàmica, la fricció. Aquests models ens van permetre utilitzar controladors coneguts com "feed-forward", on podem canviar activament els guanys buscant l'equilibri precisió-suavitat que més convingui. A més, hem usat aquests models per a inferir les forces externes actuant en el robot, sense la necessitat de sensors de força. Més endavant, ens hem adonat que els robots bimanuals han de coordinar els seus components (braços) i ser capaços d'adaptar-se a noves situacions amb facilitat. Al llarg de l'última dècada, diverses aplicacions per aprendre tasques motores robòtiques amb èxit han estat publicades. No obstant, degut a la complexitat d'un sistema complet que inclogui tots els elements necessaris, la majoria d'aquestes aplicacions consisteixen en robots més aviat simples amb costosos sensors d'última generació, o a resoldre tasques senzilles en un entorn molt controlat. Utilitzant el nostre treball en cinemàtica i control, ens hem basat en dos tipus de primitives de moviment per caracteritzar la motricitat robòtica. Aquestes primitives de moviment són molt adequades per usar aprenentatge per reforç. En particular, hem usat la búsqueda directa de la política, un camp de l'aprenentatge per reforç que usa la parametrització del moviment com la pròpia política. Per tal de millorar la velocitat d'aprenentatge en aplicacions amb robots reals, hem generalitzat un algoritme de búsqueda directa de política per a donar importància a les mostres amb mal resultat, i hem donat especial atenció a la reducció de dimensionalitat en la parametrització dels moviments. Hem reduït la dimensionalitat amb mètodes lineals, utilitzant les recompenses obtingudes EN executar els moviments. Aquests mètodes han estat provats en tasques bimanuals com són plegar roba, usant dos braços antropomòrfics. Els resultats mostren com la reducció de dimensionalitat pot aportar informació qualitativa d'una tasca, i al mateix temps ajuda a aprendre-la més ràpid quan les execucions amb robots reals són costoses.Award-winningPostprint (published version

외란 및 토크 대역폭 제한을 고려한 토크 기반의 작업 공간 제어

학위논문(박사) -- 서울대학교대학원 : 융합과학기술대학원 융합과학부(지능형융합시스템전공), 2021.8. 박재흥.The thesis aims to improve the control performance of the torque-based operational space controller under disturbance and torque bandwidth limitation. Torque-based robot controllers command the desired torque as an input signal to the actuator. Since the torque is at force-level, the torque-controlled robot is more compliant to external forces from the environment or people than the position-controlled robot. Therefore, it can be used effectively for the tasks involving contact such as legged locomotion or human-robot interaction. Operational space control strengthens this advantage for redundant robots due to the inherent compliance in the null space of given tasks. However, high-level torque-based controllers have not been widely used for transitional robots such as industrial manipulators due to the low performance of precise control. One of the reasons is the uncertainty or disturbance in the kinematic and dynamic properties of the robot model. It leads to the inaccurate computation of the desired torque, deteriorating the control stability and performance. To estimate and compensate the disturbance using only proprioceptive sensors, the disturbance observer has been developed using inverse dynamics. It requires the joint acceleration information, which is noisy due to the numerical error in the second-order derivative of the joint position. In this work, a contact-consistent disturbance observer for a floating-base robot is proposed. The method uses the fixed contact position of the supporting foot as the kinematic constraints to estimate the joint acceleration error. It is incorporated into the dynamics model to reduce its effect on the disturbance torque solution, by which the observer becomes less dependent on the low-pass filter design. Another reason for the low performance of precise control is torque bandwidth limitation. Torque bandwidth is determined by the relationship between the input torque commanded to the actuator and the torque actually transmitted into the link. It can be regulated by various factors such as inner torque feedback loop, actuator dynamics, and joint elasticity, which deteriorates the control stability and performance. Operational space control is especially prone to this problem, since the limited bandwidth of a single actuator can reduce the performance of all related tasks simultaneously. In this work, an intuitive way to penalize low performance actuators is proposed for the operational space controller. The basic concept is to add joint torques only to high performance actuators recursively, which has the physical meaning of the joint-weighted torque solution considering each actuator performance. By penalizing the low performance actuators, the torque transmission error is reduced and the task performance is significantly improved. In addition, the joint trajectory is not required, which allows compliance in redundancy. The results of the thesis were verified by experiments using the 12-DOF biped robot DYROS-RED and the 7-DOF robot manipulator Franka Emika Panda.본 학위 논문은 외란과 토크 대역폭 제한이 존재할 때 토크 기반 작업 공간 제어기의 제어 성능을 높이는 것을 목표로 한다. 토크 기반의 로봇 제어기는 목표 토크를 입력 신호로서 구동기에 전달한다. 토크는 힘 레벨이기 때문에, 토크 제어 로봇은 위치 제어 로봇에 비해 외부 환경이나 사람으로부터 가해지는 외력에 더 유연하게 대응할 수 있다. 그러므로 토크 제어는 보행이나 인간-로봇 상호작용과 같은 접촉을 포함하는 작업을 위해 효과적으로 사용될 수 있다. 작업 공간 제어는 이러한 토크 제어의 장점을 더 강화시킬 수 있는데, 로봇이 여유 자유도가 있을 때 작업의 영공간에서 존재하는 모션들이 내재적으로 유연하기 때문이다. 그러나 이러한 장점에도 불구하고 토크 기반의 로봇 제어기는 정밀 제어 성능이 떨어지기 때문에 산업용 로봇 팔과 같은 전통적인 로봇에는 널리 사용되지 못했다. 그 이유 중 한 가지는 로봇 모델의 기구학 및 동역학 물성치에 존재하는 외란이다. 모델 오차는 목표 토크를 계산할 때 오차를 유발하며, 이것이 제어 안정성과 성능을 약화시키게 된다. 외란을 내재 센서만을 이용하여 추정 및 보상하기 위해 역동역학 기반의 외란 관측기가 개발되어 왔다. 외란 관측기는 역동역학 계산을 위해 관절 각가속도 정보가 필요한데, 이 값이 관절 위치를 두 번 미분한 값이기 때문에 수치적인 오차로 노이즈해지는 문제가 있었다. 본 연구에서는 부유형 기저 로봇을 위한 접촉 조건이 고려된 외란 관측기가 제안되었다. 제안된 방법은 로봇의 고정된 접촉 지점에 대한 기구학적인 구속 조건을 이용하여 관절 각가속도 오차를 추정한다. 추정된 오차를 동역학 모델에 반영하여 외란 토크를 계산함으로써 저역 통과 필터 성능에 대한 의존도를 줄일 수 있다. 토크 기반 제어의 정밀 제어 성능이 떨어지는 또 다른 이유 중 하나는 토크 대역폭 제한이다. 토크 대역폭은 구동기에 전달되는 입력 토크와 실제 링크에 전달되는 토크와의 관계로 결정된다. 토크 대역폭은 구동기 내부의 토크 피드백 루프, 구동기 동역학, 관절 탄성 등의 요인들에 의해 제한될 수 있는데 이것이 제어 안정성 및 성능을 감소시킨다. 작업 공간 제어는 특히 이 문제에 취약한데, 대역폭이 제한된 구동기 하나가 그와 연관된 모든 작업 공간의 제어 성능을 감소시킬 수 있기 때문이다. 본 연구에서는 작업 공간 제어기에서 성능이 낮은 구동기의 사용을 제한하기 위한 직관적인 전략이 제안되었다. 기본 컨셉은 작업 제어를 위한 토크 솔루션에 성능이 좋은 관절에만 추가적으로 토크 솔루션을 더해나가는 것으로, 이것은 각 관절의 가중치가 고려된 토크 솔루션이 되는 것을 의미한다. 성능이 낮은 구동기의 사용을 제한함으로써 토크 전달 오차가 줄어들고 작업 성능이 크게 향상될 수 있다. 본 학위 논문의 연구 결과들은 12자유도 이족 보행 로봇 DYROS-RED와 7자유도 로봇 팔 Franka Emika Panda를 이용한 실험을 통해 검증되었다.1 INTRODUCTION 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Contributions of Thesis . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Overview of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 BACKGROUNDS 6 2.1 Operational Space Control . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Dynamics Formulation . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.1 Fixed-Base Dynamics . . . . . . . . . . . . . . . . . . . . 9 2.2.1.1 Joint Space Formulation . . . . . . . . . . . . . 9 2.2.1.2 Operational Space Formulation . . . . . . . . . . 11 2.2.2 Floating-Base Dynamics . . . . . . . . . . . . . . . . . . . 12 2.2.2.1 Joint Space Formulation . . . . . . . . . . . . . 12 2.2.2.2 Operational Space Formulation . . . . . . . . . . 14 2.3 Position Tracking via PD Control . . . . . . . . . . . . . . . . . . 17 2.3.1 Torque Solution . . . . . . . . . . . . . . . . . . . . . . . 17 2.3.2 Orientation Control . . . . . . . . . . . . . . . . . . . . . 19 3 CONTACT-CONSISTENT DISTURBANCE OBSERVER FOR FLOATING-BASE ROBOTS 22 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2 Momentum-Based Disturbance Observer . . . . . . . . . . . . . . 24 3.3 The Proposed Method . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.4.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.4.2 External Force Estimation . . . . . . . . . . . . . . . . . . 33 3.4.3 Internal Disturbance Rejection . . . . . . . . . . . . . . . 35 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4 OPERATIONAL SPACE CONTROL UNDER ACTUATOR BANDWIDTH LIMITATION 40 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.2 The Proposed Method . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2.1 General Concepts . . . . . . . . . . . . . . . . . . . . . . . 43 4.2.2 OSF-Based Torque Solution . . . . . . . . . . . . . . . . . 45 4.2.3 Comparison With a Typical Method . . . . . . . . . . . . 47 4.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.3.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 4.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.4 Comparison With Other Approaches . . . . . . . . . . . . . . . . 61 4.4.1 Controller Formulation . . . . . . . . . . . . . . . . . . . . 62 4.4.1.1 The Proposed Method . . . . . . . . . . . . . . . 62 4.4.1.2 The OSF Controller . . . . . . . . . . . . . . . . 62 4.4.1.3 The OSF-Filter Controller . . . . . . . . . . . . 62 4.4.1.4 The OSF-Joint Controller . . . . . . . . . . . . . 67 4.4.1.5 The Joint Controller . . . . . . . . . . . . . . . . 68 4.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.5 Frequency Response of Joint Torque . . . . . . . . . . . . . . . . 72 4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5 CONCLUSION 85 Abstract (In Korean) 100박