Humanoid Robots Part 11 docx

The Design of humanoid Robot Arm based on Morphological and Neurological Analysis 243 of Human Arm Fig. 16. Circle control error output (motion 5 times repetition error) Table 2 represent the motion error measurement data of the humanoid robot arm. Through the 5 controls, we found that mean position trace error is about 4.112mm and mean position repetition error is about 0.135mm in the Table 2. Times Sampling time(ms) Sum of error(mm) Mean error(mm) 1 50 Point (5s/0.1s(100ms) 204mm 204/50 = 4.08mm 2 50 Point (5s/0.1s(100ms) 209mm 209/50 = 4.18mm 3 50 Point (5s/0.1s(100ms) 199mm 199/50 = 3.98mm 4 50 Point (5s/0.1s(100ms) 205mm 205/50 = 4.1mm 5 50 Point (5s/0.1s(100ms) 211mm 211/50 = 4.22mm Total Mean trace error : 4.112mm Mean poison repetition error : (0.1+0.2+0.12+0.12)/4 = 0.135mm Table 2. The motion error measurement data of the humanoid robot arms 6. Conclusion In this paper, we have presented the implementation and performance evaluation for SERCOS based humanoid robot arm by using morphological and neurological analysis of human arm. Moreover, we reviewed the possibility of application of these robot arms. First, we proposed robot development methodology of open architecture based on ISO15745 for “opening of humanoid robot.” Then, we verified the method of implementation of humanoid robot arm and its application to the real world. We have implemented robot arm using SERCOS communication and AC servo motor for high precision motion control; in addition, we got a mean position trace error of 4.112mm and mean position repetition error of 0.135mm as a control performance. 244 Humanoid Robots 7. References Karl Williams, "Build Your Own humanoid Robots", Tab Bookks, 2004. Christopher E. Strangio, "The RS232 Standard - A Tutorial with Signal Names and Definitions" 1993~2006. "Universal Serial Bus Specification", Compaq, Intel, Microsof, NEC, 998. Robot Bosch Gmbh, "CAN Specification v2.0", Bosch, 1991. John F. Shoch, "An Introduction to the Ethernet Specification", ACM SIGCOMM Computer Communication Review volume 11, pp 17-19, New York, USA, 1981. ISO TC 184/SC 5, "ISO 156745 - Industrial automation system and integration Part1, 1999. David G. Amaral, “Anatomical organization of the central M. King, B. Zhu, and S. Tang, “Optimal path planning,” Mobile Robots, vol. 8, no. 2, pp. 520-531, March 2001. Rainer Bischoff, Volker Graefe, "HREMES-a Versatile Personal Robotic Assistant", IEEE- Special Issue on Huamn Interactive Robots for Psychological Enrichment, pp. 1759-1779, Bundeswehr University Munich, Germany. In A. Zelinsky, "Design Concept and Realization of the humanoid Service Robot HERMES", Field and Service Robotics, London, 1998 Rainer Bischoff, "HERMES-A humanoid Mobile Manipulator for Service Task", International Conference on field and Service Robots, Canberra, December 1997. Rainer Bischoff, "Advances in the Development of the humanoid Service Robot HERMES", Second International Conference on field and Service robotics, 1999. H. Netter MD, "Atlas of Human Anatomy, Professional edition", W.B Saunders, 2006. Function blocks for motion control, "PLCopen-Technical Committee2", 2002. 13 6-DOF Motion Sensor System Using Multiple Linear Accelerometers Ryoji Onodera and Nobuharu Mimura Tsuruoka National College of Technology, Niigata University Japan 1. Introduction This chapter describes a multi degrees of freedom (hereafter, "DOF") motion sensor system in 3D space. There are two major areas where multiple-DOF motion sensors are needed. The first involves vehicles, helicopters or humanoid robots, which are multi-input multi-output objects, each having 3 DOF in all translational and rotational directions. Thus, an accurate measurement of all 6 DOF motions is needed for their analysis and control. The second area involves considering not only the translational components, but also the rotational components for 1-DOF linear motion on ground since this type of motion is always affected to a certain extent by motion along other axes, and mixed signals of translational and rotational components are detected in the case of using 1-DOF motion sensors. So far, inertial navigation systems (INS) with highly accurate gyro sensors and accelerometers have been used in the field of rocketry and aerodynamics. However, it is difficult to install such systems combined with gyroscopes and accelerometers on small robots due to their large size, weight and cost. In recent years, small vibration gyro systems and micro-machine gyro systems have been developed by using MEMS (micro-electro- mechanical system) technology. However, the sensor units which utilize these systems are not small, weighing about 6 to 10 kilograms, and in addition there are some problems with measurement accuracy and stability. In the case of multiaxial sensors, it is known that the specific problem of non-linear cross effect arises, which means that other axial components interfere with the target one, and the measured values differ from the true values due to this effect. As a result, the cross effect reduces the measurement accuracy. In addition, as a result of increasing the effect by the gain and offset errors of each axis, stability is lost. Therefore, sensor calibration is required for suppressing the cross effect, as well as for decreasing the gain and offset errors. However, in general, gyro systems cannot be calibrated in isolation, which needs special equipments, such as an accurate rotary table, for generating a nominal motion. Thus, a proper calibration of the multiaxial sensors by the user is extremely difficult. In the present work, we propose a newly developed 6-DOF motion sensor using only multiple accelerometers, without the gyro system. The advantage of using accelerometers is that they can be calibrated with relative ease, using only the gravitational acceleration without any special equipment. So far, we have performed several experiments using the Humanoid Robots 246 prototype sensor, and observed rapid divergence followed by the specific cross effect in the multiaxial sensors. Therefore, in this chapter, we investigate these two problems of divergence and cross effect. Regarding the divergence, we analyzed the stability based on the geometric structure of the sensor system. Furthermore, we analyzed the cross effect with respect to the alignment error of the linear accelerometer, and proposed a relatively easy calibration method based on the analytical results. Finally, we investigated the proposed system and methods in an experiment involving vehicle motion, which is particularly prone to the cross effect, and demonstrated that this sensor system (i.e., the 6-DOF accelerometer) performs well. 2. Measurement principle and extension to multiple axes First, we consider the acceleration which occurs at point i on a rigid body (Fig.1). We define a position vector for the moving origin of the body ( b Σ ) relative to the reference frame ( o Σ ) as T bz o by o bx o b o ppp ][=p , and the position vector of the point i relative to the body origin as T iz o iy o ix o i o rrr ][=r . Then, the position vector b o p from o Σ is is represented as follows: . i o b o i o rpp += (1) When the rigid body revolves around the origin b Σ , Eq.(1) is written as . i o b o b o i o rωpp ×+= &&& (2) Moreover, we can rewrite the equation by taking into consideration the gravitational acceleration as follows: ( ) . i o b o b o i o b o b o i o rωωrωgpp ××+×++= &&&&& (3) Equation (3) represents the acceleration of point i on the body. If one linear accelerometer is installed at point i, the accelerometer output a i is Fig. 1. Acceleration at point i on a rigid body Σ o Σ b o ω b o p b o p i o r i o u i i g R igid Body Gravitationa l acceleration y x z Σ 6-DOF Motion Sensor System Using Multiple Linear Accelerometers 247 Fig. 2. Model of the proposed 6-DOF measurement system [] (){} , i o b o b o T i o b o b o i o T i o T i o i o T i o i a rωωu ω gp Ruu pu ××+ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡+ = = & && && (4) where . 0 0 0 ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − − − = ix o iy o ix o iz o iy o iz o i o rr rr rr R (5) Here, T iz o iy o ix o i o uuu ][=u is the sensitivity unit vector. In Eq.(3), the translational, rotational, centrifugal and gravitational accelerations are mixed, and cannot be separated using only one accelerometer output. In order to obtain 6-DOF acceleration data (i.e., data regarding translational and rotational motion), we need to resolve multiple acceleration signals, when more than six linear accelerometers are needed. Thus, in the six accelerometers, each output is given by (see Fig.2) [rad]3/2π [rad]3/4π Σ b r x b y b z b bx o ω & bz o ω & bx o p && by o p && bz o p && a 1 a 3 a 2 a 4 a 6 a 5 Dual-axis Accelerometer Sensitivity direction b y o ω & Humanoid Robots 248 ( ){} (){} (){} , 66 22 11 6 2 1 ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ×× ×× ×× + ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ + = ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ rωωu rωωu rωωu ω gp R o b o b o T o o b o b o T o o b o b o T o b o b o o a a a M & && M (6) where . 666 222 111 ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − − − = Ruu Ruu Ruu R o T o T o o T o T o o T o T o o MM (7) R o is a gain matrix which depends on the direction of the sensitivity vectors and position vectors. R o is a known constant matrix. If R o is a non-singular matrix, Eq.(6) can be written as ( ) , 0 0 06.0 03.0 22 6 5 4 3 2 1 1- ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − −− − ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ + bz o bx o bz o by o by o bx o by o bx o o b o b o a a a a a a ωω ωω ωω ωω R ω gp & && (8) where [] [] ., ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ + + − =+ bz o by o bx o b o bz o bx o by o by o bx o b o gp gp gp ω ω ω θ θ & & & & && && && && ωgp (9) Here, the terms consisting of angular velocities ),,( bz o by o bx o ωωω are the centrifugal acceleration components in Eq.(8). We tentatively refer to these terms as "CF terms". Furthermore, bx o θ and by o θ are the attitude angle of the x axis (roll) and the y axis (pitch), respectively. In addition, the distance r between b Σ and each accelerometer is 0.06 m. 6-DOF Motion Sensor System Using Multiple Linear Accelerometers 249 3. Stability analysis In motion sensor systems, one of the most serious problems is the drift effect. Although it occurs for various reasons (e.g., vibration or environmental temperature fluctuations), if the solutions are obtained only from the accelerometer outputs (that is, if they are represented by an algebraic equation), they can be improved with relatively high accuracy by performing sensor calibration. However, as shown in Eq.(8) of this system, the z axis acceleration is resolved only by accelerometer outputs (a 1 -a 6 ), while the x and y axis accelerations are resolved by outputs and CF terms with the cross effect in each other. In past studies, it has been indicated that these terms interact with each other, starting with the drift error. As a result, a rapid divergence of the solutions (i.e., the 6-DOF acceleration) caused by the cross effect in addition to the drift error has already been confirmed in past systems. Therefore, in order to analyze the stability of the proposed system in the same case, let us assume the measurement errors occurring as follows: ),621( , , ,,iΔaaa Δ iini b o bn o b o =+= += ωωω &&& (10) where the suffix n represents a true value, and Δ represents the combined error with gain and offset error. Here, we substitute Eq.(10) into Eq.(8) and solve the equation for the error terms ( Δ ). As a result, we obtain the following second-order differential equations for the error: , ))(()()()( )( )( )( ))(()()()( )( )( )( 2 2 ⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎨ ⎧ =+− =+− nΔaFnΔnnΔ n n nΔ nΔaFnΔnnΔ n n nΔ iyby o bzn o by o bzn o bzn o by o ixbx o bzn o bx o bzn o bzn o bx o ωωω ω ω ω ωωω ω ω ω & & && & & && (11) where we assume that the above errors are negligibly small, and thus we obtain Eq.(11) by linear approximation. .0)()( ,0)( ≈⋅ << nΔnΔ nΔ b o b o b o ωω ω (12) Equation (11) is a Mathew-type differential equation, which is known to be intrinsically unstable, and therefore we analyzed Eq.(11) by using numerical calculation in order to clarify the stability or instability conditions of the 6-DOF sensor system. The analytical result is shown in Fig.3, which shows the state of the amplitudes of the error terms ( b o Δ ω ) for the frequency ratio )2( or f zyx π ω ω ω = when time approached infinity. Here, x ω , y ω and z ω represent the roll, pitch, and yaw frequencies, respectively. This result shows the error terms increase rapidly when the frequency ratio becomes even (i.e., K0.6or0.4,0.2 or = zyx ω ω ). Humanoid Robots 250 Fig. 3. Measurement error amplitude as plotted against the frequency ratio Thus, it is considered that this system might become unstable when the roll or the pitch frequency become even for the yaw motion. However, in 3D motion of a rigid body, it is unlikely that the rigid body motion satisfies the above instability condition since the roll or pitch motion is generally synchronized with the yaw motion. This condition is likely to occur in specific cases, such as machinery vibration. Thus, conversely, it is unlikely that the system becomes unstable as a result of the above condition in a rigid body motion, such as the motion of a vehicle or an aircraft. However, the rapid divergence seen in Fig.3 is likely to occur when the system satisfies this condition due to measurement errors or the cross effect induced by the alignment error in this system. In the next section, we analyze the estimated alignment error and investigate a sensor calibration in order to minimize it. 4. Sensor calibration 4.1 Accelerometer error analysis This sensor system obtains 6 DOF accelerations by resolving multiple linear acceleration signals. Therefore, the sensitivity vector ( i o u ) and the position vector ( i o r ) of the linear accelerometers must be exact. In the previous section, we investigated the case for each accelerometer without considering the alignment errors. Therefore, in this section, we investigate the accelerometer outputs mi a by taking into account the error terms i o Δ u and i o Δ r , which constitute the alignment errors of this sensor. Additionally, since accelerometers generally have offset errors, we assume the offset error to be ofi a Δ , in which case the accelerometer outputs with these alignment errors can be written as follows: 0.0 1.0 2.0 3.0 4.0 5.0 6.0 Measurement error amplitude Frequency ratio -∞ 0 + ∞ 6-DOF Motion Sensor System Using Multiple Linear Accelerometers 251 () () (){} [] () () () [] [] , , , 621 621 T ofofofof T mmmm of T b o rvirvi b o b o oo of T i o T i o b o b o T i o T i o b o b o oo m aaa aaa ΔvecΔΔ ΔΔΔΔ ΔΔΔΔ L L & && & && = = +++ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡+ += + ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ +××++ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡+ += a a aΩcc ω gp RR arrωωuu ω gp RRa (13) where () ( ) ( ) [ ] () (){} [] (){} [] (){} [] (){} [] () () () () . ,][ , , 22 22 22 332313322212312111 333231 232221 131211 ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ +− +− +− = ××= = ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ +++=+ ++−+=+ by o bx o bz o by o bz o bx o bz o by o bz o bx o by o bx o bz o bx o by o bx o bz o by o b o b o b o T T T T i o i o T T T i o i o T T T i o i o T T T i o i o rvirvi i o i o T i o T i o T i o T i ooo aaaaaaaaa aaa aaa aaa vec ΔΔvecΔvecΔvecvecΔ ΔΔΔΔ ωωωωωω ωωωωωω ωωωωωω ωωΩ rurururucc RRuuuuRR (14) In Eqs.(13) and (14), ofi a Δ and i o Δ u are based on Table 1, and i o Δ r is based on the accuracy of the finish for the base frame. The sensor frame was cut by NC machinery. Its machining accuracy is ± 0.1 [mm] and ± 0.1 [deg] or better in a length accuracy and an angular accuracy, respectively. The results of calculating the maximum range of each term are shown in Table 2 when the above performance and accuracy are considered. As a result, the terms including i o Δ r can be omitted since they are negligibly small in comparison to the other terms, as seen clearly from Table 2. Thus, we should consider only accelerometer errors including i o Δ u , and the error terms (i.e., R o Δ and rvi Δc ) can be written as follows; ( ) { } [ ] () {} [] () {} [] ., 66 22 11 666 222 111 ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ − − − = T T T oo T T T oo T T T oo rvi o T o T o o T o T o o T o T o o Δvec Δvec Δvec Δ ΔΔ ΔΔ ΔΔ Δ ru ru ru c Ruu Ruu Ruu R M MM (15) Therefore, Eqs.(13) and (15) are sensor equations which include principal errors. Humanoid Robots 252 Measurement Range ±20 [m/s 2 ] Resolution (at 60 Hz) 0.02 [m/s 2 ] Operating Voltage Range 3 ~ 5 [V] Quiescent Supply Current 0.6 [mA] Temp. Operating Range 0 ~ 70 [degree Celsius] Size 5×5×2 [mm] Gain error |/||| j j j uu Δ ±20 [%] Absolute alignment error |,/||| j j j j u αΔ |/||| j j j j u βΔ ±1.75 [%] Offset error ga ofj /|| Δ ±200 [%] Table 1. Specifications of the dual-axis accelerometer chip (Analog Devices, Inc. Accelerometer ADXL202E) Error factor Δ o R Error definition i o i o u u max Δ i o T i o i o T i o Ru Ru max Δ i o T i o i o T i o Ru Ru max Δ i o T i o i o T i o Ru Ru max ΔΔ Estimated value 0.251 0.251 0.242 × 10 -2 0.651× 10 -3 Error factor Δc rvi Error definition ( ) { } () {} T T i o i o T T i o i o vec vec ru ru max Δ ( ) { } () {} T T i o i o T T i o i o vec vec ru ru max Δ ( ) { } () {} T T i o i o T T i o i o vec vec ru ru max ΔΔ Estimated value 0.251 0.247 × 10 -2 0.751× 10 -3 Table 2. Estimated error values 4.2 Calibration method for sensor errors In general, a sensor system is calibrated using a known reference input. In the proposed 6- DOF sensor, it is necessary to determine at least 42 ( 666 + × ) components. However, in this system, as shown in Eqs.(13) and (15), the unknown errors constitute 24 components (i.e., [...]... reserved to discussions and further works 2 Humanoid locomotion robotics 2.1 Humanoid and biped robots evolution A humanoid robot is commonly assumed to be a biped otherwise some wheeled humanoid robots are proposed by researchers (Berns et al, 1999) Humanoid robotics includes all the aspects of human like machines such as: walking, grasping, emotion or cognition, etc Humanoid locomotion robotics is interested... crucial of the independence of these robots it is also crucial to the emergence of self learning attitudes All these factors impulses the rapid growth of humanoid robotics Humanoid robots are legged robots with a limited number of two legs, such a limitation is important since it has direct impact on stability control policy When two legs are used in a 260 Humanoid Robots dynamic walking process, the... swarm optimization paradigm This proposal can be used for small size humanoid robots, with a knee an ankle and a hip and at least six Degrees of Freedom (DOF) Keywords Human gaits analysis, intelligent robotics, Humanoid robotics, Biped robots, evolutionary computing, particle swarm optimization 1 Introduction In near future humanoid robots will be asked to “live” and collaborate with humans, they have... Relative Trajectory Control Source : Source : Source : Source : 262 Humanoid Robots (b)9 (c)10 (a)8 Fig 2 Humanoid locomotion systems or biped robots, (a) BIP robot, (b) Lucy robot, (C) Robian robot 2.2 Description of the IZIMAN project “IZIMAN” is a research project aiming to propose alternative intelligent solutions to humanoid robots The IZIMAN architecture aims to propose a schema to help emergence... (t ) is the current position of the particle (i), vi (t ) (6) (7) is the particle velocity; c1 represents the moderation of particle personal contribution; c2 represents the moderation of social contribution; (r1) and (r2) are random numbers within the interval [0.0, 1] Note that p plbest represents the best particle in the particle (i) neighborhood; gbest is the particle getting the best fitness function... the COM particle assumed here by P0.0 is within the sustention polygon P0.0 represents the COM of the robot mass, it is a virtual particle and has no search swarm attached to it The swarms are conceived to work as follows: The memory particles are connected hierarchically from bottom to top, such a connection means that particle (p0.2), particle 2 of swarm 0 communicates its position to both particles... ASSIMO It is important to distinguish between full size humanoids and smaller ones Full size humanoids such as HRP2 or ASSIMO have a size which is comparable to humans Robots like Nimbro (Behnke 1 DOF : Degree Of Freedom Toward Intelligent Biped-Humanoids Gaits Generation 261 et al, 2007) or Qrio have sizes that not exceed 1m Recently a French amazing humanoid robot, called Nao, was proposed while still... amazing humanoid robot, called Nao, was proposed while still under development The Nao robot was the official platform for the IEEE Humanoid conference and Robocup competitions (a)2 (b)3 (c)4 (d)5 Fig 1 Humanoid robots: (a) and (b) are human size robots, (c) and (d) are middle size robots (a) HRP2, (b) ASSIMO, (c) Nimbro soccer robot, (d) NAO robot In Europe, some research projects have been developed in... design with a great resemblance with us Biped humanoids robots are expected to have increasing field of exploitations, they are naturally adapted to human like commodities and have the advantage to fit more the human’s environment than other kind of robots; humanoids can coordinate tasks with humans workers (Arbulu & Balaguer, 2008) with human like comportments Humanoid robotics issues include building... an increasing interest to humanoid robotics helps the development of more humanoids; small size humanoids are actually proposed for entertainments; some models can be used as low cost research validation platforms One of the earliest projects in humanoid locomotion is the Waseda university, Japan where Kato and his team build their walker robot, WL1, since 1966 By 1984 a humanoid dynamic walker is . further works. 2. Humanoid locomotion robotics 2.1. Humanoid and biped robots evolution A humanoid robot is commonly assumed to be a biped otherwise some wheeled humanoid robots are proposed. analysis, intelligent robotics, Humanoid robotics, Biped robots, evolutionary computing, particle swarm optimization. 1. Introduction In near future humanoid robots will be asked to “live”. independence of these robots it is also crucial to the emergence of self learning attitudes. All these factors impulses the rapid growth of humanoid robotics. Humanoid robots are legged robots with a