IROS2019国际学术会议论文集2000

A Spring-Aided Two-Dimensional Electromechanical Spine Architecture for Bio-Inspired Robots Bonhyun KuSunyu WangArijit Banerjee AbstractThis paper presents a distributed six-link two- dimensional electromechanical actuator that emulates a bi- ological spine. The gearless actuator is made by stacking modules of E-shaped cores along with integrated springs. A coil excitation induces magnetic fl ux in the core, which produces electromechanical force in the air gap between two adjacent cores. The proposed actuator is driven by dc-dc converters with current control. Electromechanical force analysis for the proposed spine architecture with different air-gap distances and spring analysis that improve the actuators performance are discussed. Experimental results show different biological motions with a prototype design. The prototype can produce a maximum torque of 1.4 N-m. I. INTRODUCTION An articulated spine signifi cantly enhances agility, stability, and energy effi ciency in robotic systems 1. Inspired by some of the fastest animals such as horses 2 and cheetahs 3, several robot designs have incorporated articulated spines to increase their range of motion and performance 4. For example, the active spine in “Bobcat” 5 allows fast locomo- tion and high stability during forward movement. Compar- isons between fl exible-unactuated and rigid-non-deformable quadruped torsos have shown that a compliant spine promotes locomotion effi ciency by facilitating leg recirculation and reducing the cost-of-transport at relatively high speeds 6. Articulated spines in humanoids can potentially save 26.5% of total energy consumption for certain walking patterns by reducing the center-of-mass movement 7 while simultane- ously aiding in balancing the body 8. In amphibian- 9, lizard- 10, and fi sh-inspired robotic systems 11 articulated spines enable locomotion to appear elegant, aesthetically pleasing, and natural 12. A spine mechanism is remarkably different from other standard robotic joints, such as an arm or limb, due to the presence of a multiplicity of single-joint segments, each with a limited range of motion. For example, a study of fourteen vertebrae from four-year-old sheep weighing between 57 and 81 kg showed that the range of motion for single-joint segments varied between 6 and 10 degrees, particularly in the upper and middle thoracic spine region with applied moments of 7.5 N-m 13. Similar studies on human sub- jects show a range of lateral bending of 3-10 degrees 14. Department ofElectricalandComputerEngineering,University ofIllinoisatUrbana-Champaign,Urbana,IL,USAbonhyun2, Department ofMechanicalScienceandEngineering, UniversityofIllinoisatUrbana-Champaign,Urbana,IL,USA Prior approaches to create an articulated spine have relied on using conventional actuators: geared dc motor 15, tendon- driven 16, pneumatic 17, tendon-driven elastic continuum 18, and shape memory alloys (SMA) 19. However, these conventional actuators have several drawbacks. Dc motors with gears have poor backdrivability caused by friction and refl ected inertia due to the gears 20. Moreover, the presence of small gaps between mechanical parts causes backlash. In a synthetic spine, a small backlash leads to a signifi cant reduction in angular accuracy because of the limited rotation angle. Tendon-driven actuators produce strong tension, but their compression force is relatively weak. SMA actuators have a slow response time, and pneumatic actuators require extra equipment, e.g., an air compressor. This paper presents a spring-aided two-dimensional elec- tromechanical spine architecture that is modular, scalable, and has a simple mechanical structure, as shown in Fig. 1. The elctromagnetic design trade-offs of the actuator have been presented in our previous research 21. This paper extends the previous research by integrating mechanical springs to improve the reduced torque capability at large inter-module air-gap distances. A set of springs is added on either side between individual modules to enhance the actuators torque capability. Section II introduces the system overview, analytical model, wedged joint design, and spring design of the pro- posed actuator. Section III presents simulation results with springs and their analysis. Section IV shows the experimental setup and results. II. DESIGN OF ASPRING-AIDEDDISTRIBUTED ELECTROMECHANICALACTUATOR In this section, electromagnetic force induced by the coil current is analyzed. After describing an analytical model, Fig. 1: Proposed actuator: Six E-core modules are stacked, and springs are used on both sides between adjacent modules. 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 IEEE793 a wedged joint design is discussed. The joint assists both the mechanical structure and the electromagnetic design. Restoring torque in the previous spring-less design was signifi cantly low 21. For example, when the adjacent E-core is fully rotated to one side, the air gap on the other side is at maximum. Relying only on electromagnetic force resulted in poor torque capability with increasing air-gap distance. Extension springs have been added on either side of each single module to improve the torque capability. A. System Overview The actuator is a stack of E-cores utilizing electromagnetic force induced by controlled current through coils, while varying the air-gap distances between adjacent modules. The E-core serves as the main mechanical structure, the fl ux- carrying element, and the heat sink for the power converters. Two dc-dc buck converters control each coil current in a single module. When the left coil is excited in single-module operation, the upper link rotates counter-clockwise; when the right coil is excited, it rotates clockwise. Coils are alternately excited because the electromagnetic force is always attractive regard- less of the excitation. The coil holders are 3D-printed with a friction-fi t feature. Power electronic devices are mounted on the core to utilize it as a heat sink for the two dc- dc converters. The core material, Hiperco50A, allows high saturation fl ux density, resulting in high torque capability. A pin, located at the center between two connected modules, is the actuators axis of rotation. Additionally, two clamps function as the fi xture for the spine. Clamp dimensions have been determined so that the magnetic path area at the joint along the x-, y-, and z-axes is identical to the core cross-sectional area. The clamp is made of the same material as the E-core. Adjacent E-cores are physically and electromagnetically connected via clamps. The I-shaped core is used to provide the fl ux path for the last module, as shown in Fig. 1. B. Analytical Model for a Single Module Only one coil excitation is considered in the analytical model, because the two coils in each module are always excited alternately. Magnetic reluctance of the actuator varies as a function of the air gap. Reluctance R regarding the air- gap distances and average magnetic fl ux-path length in the core is R(g) = g 0Ac + l 0rAc = 1 0Ac ? g + l r ? (1) where 0is the air permeability, ris the relative core permeability, Acis the core cross-sectional area, g is the air- gap distance, and l is the average magnetic fl ux path length in the E-core. Magnetomotive force (mmf) F is F = NI(2) where N is the number of turns in a coil, and I is the coil current. Using (1) and (2) above, the electromagnetic force f is obtained as 22 f = 1 2F 2 d dg ? 1 R(g) ? = 1 2 0AcN2I2 ? g + l r ?2. (3) Since the air-gap distance of the proposed actuator changes, electromagnetic force of the actuator depends on the air gap as well. A negative sign indicates that the force is in the direction that decreases the air-gap distance. The air gap g is relatively much greater than l/r, since the relative core permeability is high when the core is not saturated. Therefore, the l/rterm becomes negligible unless the core is saturated. As noticed in (3), the force is inversely proportional to the air- gap distance g squared. Therefore, a smaller air-gap distance leads to a higher electromagnetic force. The actuators wedge-shaped air gap creates a non-uniform air-gap distance that results in partial core saturation when the air gap is small. Because of core saturation, the decreased rleads to a limited amount of force. Partial core saturation caused by this non-uniform air-gap distances. Thus, core saturation is addressed through distributed air-gap analysis 21. C. Wedged Joint Design Air permeability compared with the E-core imposes con- straints on the joints mechanical design. Thus, the joint design must minimize the air-gap volume in the systems magnetic fl ux at a given maximum rotational angle between two adjacent E-cores. A wedged joint has been designed to eliminate the air gap. The designed joint also maintains constant contact between the two adjacent E-cores, as they slide tangentially on the base E-core. D. Spring Mechanism Design A spring mechanism has been designed to increase the systems torque output at its most disadvantageous angle by sacrifi cing the torque output at its most advantageous angle. Linear extension springs, chosen to fi t the actuators size, are mounted on the outer side of the coil holders to prevent Fig. 2: Three linear extension springs are attached to each side of module. 794 Fig. 3: Linear extension spring mechanism. disturbance to the magnetic fl ux path in the core. The spring mechanism consists of three linear extension springs with hook ends, two steel pins, and a pair of mounting bases integrated in the coil holders, as shown in Fig. 2. The spring hook ends are attached to the two steel pins, which are fi xed on the coil holders. Three slots on the mounting base match the springs wire diameter and prevent them from sliding. The hook ends, steel pin, and slots form a revolute joint. This ensures that when the springs are extended, their motion is linear and in line with the system motion. Initial tension is given to the springs to avoid discontinuous force change within the range of motion. When two adjacent E-core modules are at neutral angular position relative to each other, the extension springs on both sides of the center symmetry axis are stretched by the same amount, generating zero net moment. When they deviate from their neutral angular position, the springs on either side are elongated by different amounts, generating a net moment that always tends to restore the neutral angular position. In the coordinate system defi ned in Fig. 3, the spring mechanism effect on the upper moving E-core module is equivalent to that of a torsion spring with 0.2766 N-m/degree spring rate. It can be precisely tuned through the number of parallel extension springs and the distance from the spring attachment pin to the center joint, which is the magnitude of line segment OA in Fig. 3. Torque characteristics of the actuator without springs and with springs are shown in Fig. 4 and 5, respectively. They are based on fi nite element analysis (FEA) simulation. Positive torque indicates that a module experiences clockwise rota- tion, and negative torque means counter-clockwise rotation. Variables are the angular position of the upper module and the coil current. The angle is varied from -4.5 degrees to 4.5 degrees, and the current is varied from 0 A to 3 A. In Fig. 4, maximum torque is 2.4 N-m at 4.5 degrees, and minimum is 0.14 N-m at -4.5 degrees. When the angle is close to -4.5 degrees in Fig. 4(a), the actuator has poor torque capability. Figure 4(b) shows the current versus torque profi le for the module. Since the system without springs is highly non-linear, and provides limited torque when the air gap is large, linear extension springs are used to improve the torque capability at large air-gap distances as described in Fig. 2. An analytical (a)(b) Fig. 4: Torque capability of the actuator without springs. The color bar indicates torque in N-m: (a) Torque versus angle. (b) Torque versus current. (a)(b) Fig. 5: Torque capability of the actuator with springs. The color bar indicates torque in N-m: (a) Torque versus angle. (b) Torque versus current. model of the spring is combined with the electromagnetic model to derive the torque-displacement characteristic of the overall module, as shown in Fig. 5. The linear spring torque line is noticeable in Fig. 5(a). Right side of the straight line is for the right coil excitation, and left side of the line is for the left coil excitation. Spring-aided actuators maximum torque is 1.4 N-m at -4.5 degrees, and minimum torque is 0.26 N-m at 2 degrees. Compared to the actuator without springs, the torque at -4.5 degrees has increased from 0.14 N-m to 1.4 N-m, and the torque at 4.5 degrees has decreased from 2.4 N-m to 1.3 N-m. In Fig. 5(a), the positive peak torque at -4.5 degrees indicates that most of the torque is provided by the springs to turn clockwise. Since the air gap is large, the induced elec- tromagnetic torque is relatively small compared to the spring torque. The negative peak torque at -4.5 degrees implies that the electromagnetic torque is much stronger than the spring torque, therefore, the module turns counter-clockwise. This is because of the small air gap at this position. Figure 5(b) shows the enhanced torque capability at low current. Overall, the spring-aided actuator has improved the torque capability when the air gap is large. The specifi cations for each module with springs are listed in Table I. E. Power Electronics and Current Control Two identical dc-dc buck converters are designed for each coil and integrated in each actuator module to control coil 795 TABLE I: Specifi cations of the proposed actuator with springs Dimensions7(L) x 3(W) x 4.2(H) cm3 Mass310 g Angular fl exibility9.15 Torque0.26-1.4 N-m Input power12 V , 1.29 A (max) SensingCurrent Fig. 6: PI current controller response from 0.5 A to 1.0 A in 6 ms. current using a PI controller. The input voltage is 12 V, and an auxiliary power supply for current sensors is included. Due to the limited space, a total of three PCBs are assembled into a set of circuits. Two buck converters are located on the lower front side of the E-core, and the coil copper wire is directly plugged into the PCB. The two major heat sources of a module are coils and MOSFET switches of the buck converters. MOSFET switches are placed on the bottom side of the buck converter so that the heat can be dissipated through thermal pad and the E-core. The purpose of the buck converter is to control coil current using PI controller. Figure 6 is the current change from 0.5 A to 1.0 A using the PI controller when two modules are in parallel. The response time is about 6 ms. F. Actuator Comparison Maxon EC 20 fl at motor, which is used in SEA Snake module 15, is compared with the proposed actuator, listed in Table II. Box volume and cylindrical volume are used for the proposed actuator and EC 20, respectively. The prototype actuator is bulkier and heavier than EC 20, however, the specifi c torque is signifi cantly higher over the entire torque range. The angular fl exibility design target of the actuator was an animals vertebra, so each module has limited angular fl exibility while the motor can make full rotation. TABLE II: Actuator comparison between the proposed actu- ator and Maxon EC 20 fl at motor 23. Proposed actuator EC 20 fl at Volume88.2 cm35.29 cm3 Mass310 g22 g Torque0.26-1.4 N-m7.74 mN-m Specifi c torque0.839-4.52 N-m/kg0.352 N-m/kg Angular fl exibility9.15 360 Power15.6 W7.90 W III. SIMULATIONS FEA models are created using ANSYS Maxwell to simu- late the magnetic fl ux and corresponding force while varying angle and coil current for each module. The rotational angle is varied from -4.5 to 4.5 degrees every 0.5 degree step. The current is varied from zero to 3 A with 400 coil turns. Figure 7 displays the magnetic fl ux inside the cores and clamps when one coil is excited at 2 A. From (3), the force increases as the air gap decreases. At a higher angle, the force does not increase as the coil current increases as expected, because of core saturation. Figure 8 shows the average fl ux density enters the saturation region as the current increases when the actuator is at the 4.5 degrees position. In the other two cases (zero and -4.5 degrees) the core does not saturate, so the average fl ux density is linear to the coil current. A. Torque Requirements for Animal-like Motions MATLAB Simscape is used to calculate the torque re- quired at each module for snake-like motion and swing motion. The series-connected six modules, including the top I-shape core are set up in the simulation. The bottom module is fi xed to simplify the analysis. The system is placed on the ground horizontally with gravity. The torque required for certain motions is calculated at the existing six joints. The Fig. 7: Magnetic fl ux is induced by the coil current when fully rotated. 796 Fig. 8: Flux density from FEA model when the angular position changes. (a) Left swing(b) Right swing(c) S-shape Fig. 9: Three different motions for six modules. torsional spring constant is also applied to each joint. Figure 9 shows three examples of motions that are left swing, right swing, and S-shape imitating an animal-like spine. Figure 10 shows each modules torque requirement for snake-like motion and left/right swing motion at 2 Hz frequency. Joints 1-6 are located from the bottom to the top link in order. Positive torque means the right coil is excited, and negative torque means the left coil is excited. The required peak torque is within the actuators torque capability. For the sinusoidal snake-like motion in Fig. 10(a), torque requirements are sinusoidal with different amplitudes, because the lower