Summary of dissertation: Developing an algorithm of navigation and control for underwater vehicles

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Constructing the methodology for synthesizing navigation algorithm and motion control algorithm for underwater vehicles equipped platform or strapdown inertial navigation system during independent motion (Autonomous).

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Nội dung Text: Summary of dissertation: Developing an algorithm of navigation and control for underwater vehicles

MINISTRY OF EDUCATION AND MINISTRY OF DEFENCE TRAINING ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY DUY TRUNG truong Developing an algorithm of navigation and control for Underwater vehicles Specialty: Control engineering and Automation Code : 65 52 02 16 SUMMARY OF DISSERTATION HAnOi 2014
Dissertation was compeleted at: ACADEMY OF MILITARY SCIENCE AND TECHNOLOGY MINISTRY OF DEFENCE Scientific supervisors: 1. Ass. Prof. Dr. Duc Thuan Tran 2. Dr. Quang Vinh Nguyen Reviewer 1: Ass. Prof. Dr. Van Nha Dinh Hanoi University of Science and Techonology Reviewer 2: Dr. Quang Hai Nguyen Navy engineering Institute Reviewer 3: Dr. Vu Nguyen Academy of Military Science and Technology This doctoral dissertation will be defended to the dissertation committee. This event is going to be celebrated at Academy of Military Science and Technology, …., 2014 Be able to be found out at: - The Library of Academy of Military Science and Technology - The National Library of Vietnam
INTRODUCTION SECTION 1. Introduction Research, development of underwater vehicles including anti- submarine weapons are importance in the development, protecting our sea and Islands. Figure 1: The motion trajectory of ASWs dropping from plane Anti-submarine weapons (ASWs) drop motion with a parasol from plane. The error between actual water touched point and calculated water touched point of ASWs including the error of opportunities release ASWs from plane and error of water touched point due to difference trajectory when ASWs drop motion with a parasol in the atmosphere. This error may exceed the operating limits of self leads equipment of ASWs so that ASWs will not detect the target (figure1). Thus, to improve target detection, ASWs should motion to the point of contact of desired trajectory. To overcome the above error, the dissertation proposed adding inertial navigation system (platform or strapdown inertial navigation system) for ASWs released from plane. The dissertation is going into two basic problems that are navigation and control of ASWs with offer additional inertial navigation system. 1
2. The goal of research: Constructing the methodology for synthesizing navigation algorithm and motion control algorithm for underwater vehicles equipped platform or strapdown inertial navigation system during independent motion (Autonomous). 3. Subject and method of the study: - The object of the dissertation research: The control system of torpedo shape autonomous underwater vehicles. - Research methodology: Applying tools and mathematical methods of modern control theory for developing navigation and control algorithms. Using simulation techniques to assess. 4. Scientific contributions and practical contributions: - The results of reseach in this dissertation are a scientific basis for constructing the software for the control system of anti-submarine weapon equipped inertial navigation system. - The results of reseach in this dissertation are the basis for improvement, modernization of the existing anti-submarine weapons and for design, manufacture new anti-submarine weapons. 5. Layout of dissertation: The dessertation has introduction section, four chapters, conclusion and two annexes. Content of the dissertation is presented in 119 A4 papers: Chapter 1. Overview of navigation and control of underwater vehicles Chapter 2. Developing an algorithm for determining navigation parameters for anti-submarine weapons Chapter 3. Proposing identification and control algorithms for anti- submarine weapons Chapter 4. Simulation of identification, navigation and control algorithms for anti-submarine weapons. 2
Chapter 1 OVERVIEW OF NAVIGATION AND CONTROL OF UNDERWATER VEHICLES 1.1 Overview of underwater vehicles The dissertation calculates the corrected trajectory of anti-submarine weapons (ASWs) dropping with a parasol from plane and controls ASWs motion follow the corrected trajectory. Thus need to constantly determine the position and attitude of ASWs during drop motion with a parasol in the atmosphere and the motion in the water environment for the correcting trajectory period. Figure 1.5: The desired and correcting trajectory of ASWs 1.2 The frames used in describing the motion of underwater vehicles Figure 1.9: Relations of the Earth frame and the local-level frame Figure 1.10: The body frame 3
1.2.1 The inertial frame The inertial frame is a frame without acceleration. 1.2.2 The Earth frame The earth frame OX eY e Z e (figure 1.9). 1.2.3 The local-level frame The local-level frame (navigation frame) OX 0Y0 Z 0 (figure 1.9). 1.2.4 The body frame The body frame Gb X bYb Z b (figure 1.10). 1.2.5 Frame transformation matrix 1.2.5.1 Euler angle method Perform three consecutive rotations according to the Euler angle ( ,  , ) to determine the cosine matrix from the body frame to local- level frame. 1.2.5.2 The method using Rodrig – Hamilton parameters Orientation cosine matrix from body frame to local-level frame can be determined by Rodrig - Hamilton parameters:  202  212  1 212  20 3 213  202   c11 c12 c13    Cbn   212  20 3 202  222  1 223  201   c21 c22 c23  (1.12)    213  20 2 223  201 202  232  1 c31 c32 c33  1.3 Overview of inertial navigation 1.3.1 Principles of inertial navigation 1.3.1.1 Platform inertial navigation Using . the platform inertial navigation equipment need to determine the orientation cosine matrix Cdn between platform frame OX DYD Z D and local-level frame OX 0Y0 Z 0 and then calculate: ( f N , f E , f D )  Cd (ndx , ndy , ndz ) T n T (1.21) VN  f N ; VE  f E ; VD  f D  g (1.22) Figure 1.14: The local-level frame and x  VN ; y  VE ; z  VD (1.23) local-level inertial navigation system 4
1.3.1.2 Strapdown inertial navigation The Rodrig - Hamilton parameters of matrix Cbn can be wrote:  20  1 p  2 q  3 r; 21  0 p  3 q  2 r  (1.26) 22  3 p  0 q  1r ; 23  2 p  1q  0 r  The components of acceleration in local-level frame: f  Cbn ab (1.27) The velocities and coordinates of the center of ASWs are determined by equations (1.22) and (1.23). However, the measured values of micromechanical gyroscopes including noise and drift, the measured values of accelerometers including noise. So if used directly measured values of micromechanical gyroscopes and accelerometers, the navigation parameters will have error and it is increased overtime. 1.3.2 Combination of positioning and navigation systems There are some combining methods of positioning system are proposed to fix the error by using direct information from the accelerometer and gyroscope micromechanical parameters to determine navigation parameters. This dessertation proposes the addition measured equipment and applied the nonlinear extended Kalman filter (Figure 1.15). Figure 1.15: The nonlinear extended Kalman filter 5
1.4 Autonomous underwater vehicles dynamic modeling 1.4.1 Inertial, centripetal forces and moments of autonomous underwater vehicles Analysis of forces and moments of autonomous underwater vehicles to determine inertia matrix M RB and centripetal matrix CRB . 1.4.2 External forces and moments of autonomous underwater vehicles 1.4.2.1 Gravitational, bouyancy forces and moments Gravitational, bouyancy forces and moments g ( ) are presented in the body frame 1.4.2.2 Added mass forses and moments Analysis of forces and moments of added mass allows us to identify the inertial matrix and centripetal matrix of added mass M A , C A . 1.4.2.3 Hydrodynamic forces and moments Analysis of drag and lift forces of autonomous underwater vehicles, hydrodynamic forces and moments D(  ) are determined. 1.4.2.4 Rudders forces and moments Analysis of rudders forces and moments of autonomous underwater vehicles, forces and moments vector  bl and parameters of forces and moments of rudders L(  ) follow body frame axis are determined. Generated thrust of autonomous underwater vehicles is  pl . 1.4.3 Effect of environment to autonomous underwater vehicles Autonomous underwater vehicles operate in the water environment so that only current is consider. 1.5 Conclusions of chapter 1 1. Missiles and torpedoes (anti-submarine weapons) are important weapons in the modern war. However, in the control system of anti- submarine weapons at Vietnam don’t have inertial navigation system so when combat in complex weather conditions are difficult. So we need to improve and modernize by equipping inertial navigation system and resolving some academic issues. 6
2. Equipping Strapdown inertial navigation system take advantage of cheaper price. However, should have some solutions to overcome the disadvantages that the manufacturing technology can not solve that is the diff of measured values of inertial navigation system. Adding measured devices requires accompanying synchronized processing algorithms. This issue is still new and there are many different implemented solutions. 3. Equipping platform inertial navigation system have a high cost but to customize overcome the drawbacks of Strapdown inertial navigation system. However, should develop the algorithms for determining the direction cosine matrix between platform frame and local-level frame. This is a new problem at Vietnam. The foreign documents when handover weapons didn’t mention this issue. So need to research the problem for determining the direction cosine matrix between platform frame and local-level frame when using platform inertial navigation system. 4. Correcting trajectory of anti-submarine weapons equipped inertial navigation system needed to develop control algorithms for anti- submarine weapons during the motion in the water environment to the point of contact of desired trajectory to ensure probability of target destruction is the greatest. Chapter 2 DEVELOPING AN ALGORITHM FOR DETERMINING NAVIGATION PARAMETERS FOR ANTI-SUBMARINE WEAPONS 2.1 Developing Strapdown inertial navigation algorithm for anti- submarine weapons 2.1.1 Developing an algorithm for determining navigation parameters for anti-submarine weapons during drop motion in the atmosphere Application of nonlinear extended Kalman filter estimating Rodrig – Hamilton parameters base on measures values from micromechanical gyros, accelerometers and magnetometers (figure 2.4), then determining 7
the direction cosine matrix follow (1.12), the attitude follow (1.15), the velocities and coordinates of the center of ASWs follow (1.22) and (1.23). Measuring R Q EKF devices Adjusting 3 Micromechanical matrix K k gyros Zk Xˆ (  ) k 3 Magnetometers Kk Fk 1 ( Xˆ (  ) ) k 1 3 Accelerometers Zˆ k Xˆ () k ax a y az hk ( Xˆ (  ) ) k n Determining navigation parameters Xˆ (  ) k C b M 0 , 1 , 2 , 3   212  20 3    arctg   fE fN fD  20  21  1   2 2    arcsin(213  20 2 )  22 3  20 1     arctg    20  23  1  2 2 VD (0) VD g  z (0) z   VE (0) VE  y (0)   y VN (0) VN  x(0)   x Figure 2.4: The diagram used to determine navigation parameters by combining micromechanical gyros, accelerometers and magnetometers 8
2.1.2 Developing an algorithm for determining navigation parameters for anti-submarine weapons during the motion in the water environment Application of nonlinear extended Kalman filter estimating Rodrig – Hamilton parameters, the velocities in local-level frame and the depth of ASWs base on combining of micromechanical gyros, accelerometers, magnetometers, speedometers and a depth pressure sensor (figure 2.5), then determining coordinates x, y of the center of ASWs follow (1.23). Figure 2.5: The diagram used to determine navigation parameters by combining micromechanical gyros, accelerometers, magnetometers, speedometers and a depth pressure sensor 9
2.2 Developing platform inertial navigation algorithm for anti- submarine weapons 2.2.1 Developing an algorithm for determining the cosine matrix between platform frame of local-level inertial navigation system and local-level frame by coordinating of the velocity vector when releases anti-submarine weapons from the jets When ASWs on the jets, the Rodrig- Hamilton parameters of direction cosine matrix between platform frame and local-level frame: 20  N 1  E 3  D 2 (2.86) 21  N 0  E 2  D 3 (2.87) 22  N 3  E 1  D 0 (2.88) 23  N 2  E 0  D 1 (2.89) Figure 2.6: Relations of frames Application of nonlinear extended Kalman filter estimating 0 , 1 , 2 , 3 parameters and then determining direction cosine matrix Cdn between platform frame and local-level frame when ASWs on the jets. 2.2.2 Developing an algorithm for determining the cosine matrix between platform frame of local-level inertial navigation system and local-level frame by coordinating of the velocity vector when drop anti-submarine weapons from the helicopters The equations describing the velocity of ASWs: VN  c11nx  c12 ny  c13nz  (c11w 4  c12 w 5  c13 w 6 ) (2.130) VE  c21nx  c22 ny  c23nz  (c21w 4  c22 w 5  c23 w 6 ) (2.131) VD  c31nx  c32 ny  c33nz  (c31w 4  c32 w 5  c33 w 6 )  g (2.132) Implement integration both sides of the equation (2.130 – 2.132) during the period from 0 to T, from T to 2T and from 2T to 3T, constructing a linear algebraic equations system to determine the 10
elements cij (i  1, 3; j  1, 3) of direction cosine matrix Cdn between platform frame and local-level frame when ASWs on the helicopters. 2.2.3 Navigation algorithm Determining direction cosine matrix between platform frame and local-level frame when ASWs still on the plane, navigation algorithm will be processed after ASWs released from plan (figure 2.8). Relation of body frame and local-level frame is description:  c11* c12* c13*   * *  Cbn  (Cdb ) 1 Cdn  c21 * c22 c23  (2.149) c31 * * c32 *  c33   Figure 2.8: The diagram of platform inertial navigation system 11
2.3 Conclusions of chapter 2 1. Due to the inertial measured elements always practical drift and measured noise, those factors will cause errors when determining the navigation parameters. So need to use other measured devices to calibrate the measured errors. This is really a new problem in Vietnam and also urgent for exploiting, using or developing, production anti- submarine weapons. Because this issue is a matter of military secrets should be less published, require private researches of Vietnam. 2. The dissertation develops an algorithm for determining navigation parameters for anti-submarine weapons during drop motion with a parasol in the atmosphere on the basis of combination micromechanical gyros, accelerometers and magnetometers and motion in the water environment by combining micromechanical gyros, accelerometers, magnetometers, speedometers and a depth pressure sensor. The combining algorithms of the measuring devices has solved the drift of strapdown inertial navigation system. This is a new contribution of the dissertation and was published in the papers [6], [7], [8], [14], [15] of the author. 3. Platform inertial navigation algorithm are related to determining the direction cosine matrix between platform frame and local-level frame. This problem is a complex issue and has not been widely publicized, especially when anti-submarine weapons released from plane. 4. The dissertation has developed algorithms for determining the direction cosine matrix between platform frame and local-level frame of local-level inertial navigation system by using the velocity information from the plane in both cases, anti-submarine weapons drop from the helicopter and from jet. This is a new contribution of the dissertation and was published in the paper [10] of the author. 12
Chapter 3 PROPOSING IDENTIFICATION AND CONTROL ALGORITHMS FOR ANTI-SUBMARINE WEAPONS 3.1 Equations of motion of anti-submarine weapons 3.1.1 General 6 degrees of freedom equation of motion Dynamic equation of ASWs can be written as:   J ( )    1 1 1 T   M ( )C (  ,  )  M ( ) g ( )  M ( ) J ( ) pl (3.13)  1 T   M ( ) J ( )bl  3.1.2 Equations of motion follow planes 3.1.2.1 Equation of motion in the vertical plane Motion equation of ASWs follow pitch angle:   q    q  ( I yy  M q ) [ M w w  M uwutd wtd  M uq utd q  zb B sin  1 (3.19)    xb B cos  ]  ( I yy  M q ) 1 M uu utd2  s s 3.1.2.2 Equation of motion in the horizontal plane Motion equation of ASWs follow yaw angle:   r    r  ( I zz  N r ) [ N v v  N uv utd vtd  N ur utd r ] 1 (3.22)   ( I zz  N r ) 1 N uu utd2  h  h 3.1.2.3 Equation of motion follow roll angle Motion equation of ASWs follow Roll angle:   p  (3.23)   p  ( I xx  K p ) zb B sin   ( I xx  K p ) Kuu utd  1 1 2 l l 3.2 Model identification of anti-submarine weapons Simple model without loss of generality chosen as quadratic model Auto-Regressive-eXternal input (ARX): y(k )  a1 y(k  1)  a2 y(k  2)  b1u (k  1)  b2u (k  2)  d (k ) (3.24) 13
Figure 3.2: The diagram of model parameters identification algorithm by recursive least squares method 3.3 Direct adaptive fuzzy – neural output feedback control of anti- submarine weapons Figure 3.3: The diagram of a direct adaptive fuzzy - neural output feedback controller 14
Input controls are rudders angle u  ( h ,  s ,  l )T ; outputs system are Yaw angle, Pitch angle and Roll angle y  ( ,  ,  )T of ASWs measured by inertial navigation system. Control law of a direct adaptive fuzzy-neural output feedback controller is proposed (figure 3.3): u  u f  v (3.39) Where the control term v is employed to compensate the external disturbance and the modeling error, control component u fk is calculated by using the configuration of a fuzzy-neural approximator. Output of the fuzzy-neural network can be expressed as: h 2   [  ki i Akj (eˆkj )]  kT  k ( eˆk ) i 1 j 1 u fk  h 2 (3.42)  [  i Akj (eˆkj )] i 1 j 1 Where  k are connecting parameters between layer 3 and layer 4 of a fuzzy-neural approximator, Those parameters are update by adaptive law:  if || k || m or   k k1 k k  ˆ k E ( e ) k   (|| k || m and Ek 1kT k ( eˆk )  0) (3.62)  k Pr( k Ek 1k ( eˆk )) if || k || m and Ek 1k k ( eˆk )  0 T k Ek 1kT k ( eˆk ) Pr( k Ek 1k ( eˆk ))   k Ek 1k ( eˆk )   k k (3.63) || k ||2 3.4 Navigation for anti-submarine weapons to correct trajectory after touching water 3.4.1 Navigation method for anti-submarine in the horizontal plane Calculating the desired yaw angle so that the trajectory of the anti- submarine weapons follow the the corrected trajectory from the start point of controlling to the intersection point between the acceptable sphere surface and the desired trajectory. 15
3.4.2 Navigation method for anti-submarine in the vertical plane Calculating the desired pitch angle so that the trajectory of the anti- submarine weapons follow the the corrected trajectory from the start point of controlling to the intersection point between the acceptable sphere surface and the desired trajectory. 3.5 Conclusions of chapter 3 1. Due to maintain the roll angle around zero, it can be able to analyze the motion of anti-submarine weapons in two motion components: the motion in the vertical plane and in the horizontal plane. Application of the model identification method and the available control method to synthesize the control commands for anti-submarine weapons. This content was published in the paper [5] of the author. 2. Application identification algorithm by recursive least squares method can get model parameters describing the motion in two planes of anti-submarine weapons bases on data inputs are rudders angle and data outputs are yaw angle and pitch angle from inertial navigation system. The identified parameters are important for synthesizing control commands. This is a new contribution of the dissertation and was published in the paper [9] of the author. 3. Combining the information about positioning parameters of anti- submarine weapons from inertial navigation system and information, the coordinates of the point of contact with desired trajectory, the acceptable sphere radius, coordinates and desired attitude of anti- submarine weapons at the intersection point between the desired trajectory and the surface of the acceptable sphere can calculate the desired yaw and pitch angles so that the trajectory of the anti-submarine weapons will follow the desired trajectory. 4. From information about attitude of anti-submarine weapon allows synthesis the control commands according to direct output feedback adaptive neural-fuzzy control law. Rolling information from the inertial navigation system enables additional control signal for rudders angle to stabilize the rolling around zero to maintain the independence of the two movements in vertical and horizontal planes. This is a new contribution of the dissertation and was published in the papers [11], [13], [14] of the author. 16
Chapter 4 SIMULATION OF IDENTIFICATION, NAVIGATION AND CONTROL ALGORITHMS FOR ANTI-SUBMARINE WEAPONS 4.1 Simulation of determining navigation parameters for anti- submarine weapons 4.1.1 Constructing dynamic function and observer function Constructing dynamic function and observer funtion. 4.1.2 Kalman filter implementation Implementing the procedure of nonlinear extended Kalman filter. 4.1.3 Simulation results 4.1.3.1 When anti-submarine weapons drop motion in the atmosphere Simulating the algorithm of determining navigation parameters base on combination of micromechanical gyros, accelerometers and magnetometers, the results show on the figure 4.1. Figure 4.1: Rodrig-Hamilton parameters when anti-submarine weapons drop motion in the atmosphere 4.1.3.2 When anti-submarine weapons motion in the water environment Simulating the algorithm of determining navigation parameters base on cobination of micromechanical gyros, accelerometers, magnetometers, speedometers and a depth pressure sensor, the results show on the figure 4.3. 17
Figure 4.3: Rodrig-Hamilton parameters when anti-submarine weapons motion in the water environment 4.2 Simulating the determining cosine matrix between platform frame of local-level Inertial Navigation System and local-level frame by coordinating of the velocity vector. 4.2.1 In case dropping anti-submarine weapons from plane Figure 4.5: The real and estimated values of 0 , 1 , 2 , 3 The simulation results on the figure 4.5 in case ASWs released from the jet showed that estimated Rodrig – Hamilton parameters comply with assumtion parameters. 4.2.2 In case dropping anti-submarine weapons from helicopter After collecting data, calculating the parameters cij showed the results as figure 4.6. 18