Summary of Doctoral Dissertation on Electronic and Telecommunication Technique

The thesis aims to propose some control techniques for mobile target Robot-camera. After that, I studied some of the torque control techniques of joints for the Robot-camera system sticking to the mobile target and the Robot-camera system, paying attention to the motivating motor sticking to the mobile target. Finally, the author also proposed some control algorithms for Robotic-camera arm system with irregular model, external noise and preventing system degradation, using nonlinear sliding controller (TSMC) in combination with Artificial neural networks to estimate uncertain numbers.

MINISTRY OF EDUCATION AND TRAINING VIET NAM ACADEMY OF SCIENCE AND TECHNOLOGY GRADUATE UNIVERSITY OF SCIENCE AND TECHNOLOGY Nguyen Tien Kiem DEVELOPMENT RESEARCH IN SOME INDUSTRIAL ROBOTIC CONTROL ALGORITHMS WITH MANY UNCERTAIN PARAMETERS Major: Control Technique and Automation Code: 9.52.02.16 SUMMARY OF DOCTORAL DISSERTATION ON ELECTRONIC AND TELECOMMUNICATION TECHNIQUE Hanoi – 2018 The dissertation is completetd at Graduate University of Science and Technology and Vietnam Academy of Science and Technology Scientific Instructor 1: Doctor Pham Minh Tuan Scientific Instructor 2: Doctor Nguyen Tran Hiep Review 1: … Review 2: … Review 3: … The dissertation is defensed at the Council of Doctoral Dissertation Evaluation - Graduate Universty level at Vietnam Academy Science and Technology at … on date … month ….year 2011 The dissertation can be found at: - The library of Graduate University of Science and Technology - National Library of Vietnam INDEX PREFACE CHAPTER OVERVIEW 1.1 Overview 1.2 Some applications for robot CHAPTER SIMULATING PREFENRENTIAL MOTIONS FOR MOBILE ROBOTIC ARM AND DESIGNING OF SERVOING VISUAL FOLLOWING FLYING OBJECT 2.2 Simulating preferential motions of camera on machine hand and designing of servo visual system following flying object 2.2.1 Description of coordinates 2.2.2 Preferentail motion CHAPTER SPEED CONTROL FOR ROBOTIC CAMERA SYSTEM FOLLOWING MOBILE TARGETS WITH MANY UNCERTAIN PARAMETERS 3.2.1 Abstract 3.2.2 Building control algorithms following mobile targets 3.2.3 Control algorithms visual servoing for pan/tilt base with many uncertain parameters 3.2.5 Conclusion on proposed control method 13 CHAPTER CONTROL ALGORITHMS FOR INDUSTIAL ROBOTS USING ARTIFICIAL NEURAL NETWORK WITH ATTENTION TO THE ACTUATOR 14 4.2.1 Control of robotic camera system following mobile targets with attention to the impact of the actuator 14 4.2.3 Control following mobile targets using neural network 15 4.2.4 Result of simulating visual servo system with engine model/ simulation on Matlab 16 4.2.5 Conclusion on proposed control method 18 CHAPTER NON-LINEAR ADAPTIVE SLIDE CONTROL AGAINST DEGENERATION FOR ROBOTIC CAMERA WITH THE UNCERTAIN AND EXTERNAL NOISE MODEL 19 5.3 Kinetic model for robotic arm with fixed n-DOF 19 5.4 Designing control law 19 5.6 Simulating control method 21 5.7 Conclusion on proposed control method 24 CONCLUSION OF THE DISSERTATION 25 PREFACE The necessity of the dissertation Controlling robot is still problematic due to the complexity, the nonlinearity and the uncertainty of the dynamical and kinetic equations caused by robots Recently the controlling problem for robots with many uncertain parameters has received a lot of attention from researchers Hence the researcher chooses the topic "Development research in some industrial robotic control algorithms with many uncertain parameters" Research targets for the dissertation Proposing some control algorithms for robot-camera system following flying target After doing research on some of control techniques of torque joints for the robot-camera system follows the mobile target and the robot-camera system with attention to the actuator following the mobile target Finally, the author also proposes some control algorithms for robotic-camera arm system with uncertainty, external noise system against the degradation of the system, using nonlinear sliding mobile controller (TSMC) in combination with artificial neural networks to estimate uncertain parameters Some main contents of the dissertation - Develop an algorithm to control the robot-camera system mounted on a mobile platform following the target - Develop an algorithm to control the robot-camera system in consideration the uncertain parameters using artificial neural networks with control signals for joints as torque signals - Develop an algorithm to control the robot-camera system including many uncertain parameters of the kinetic model and the mobile target with attention to the actuator using artificial neural networks - Develop an algorithm to control the robot-camera system when there is uncertainty of the model and external noise using adaptive sliding control method and artificial neural network againts the degradation of the controller CHAPTER OVERVIEW 1.1 Overview Robots are used in many different areas such as simple turtle robots for teaching at high schools, welding robots in automobile factories, remote control robotic arms on the spaceship Each application has its own problems, so the research field of robotics has actually emerged There are many new emerging industries and many research results in this field while many more fields need to be explored and researched in the future along with many new perspectives that need to be developed and researched in laboratories While people think that robotics is a unique field rather than a practical application, it is actually applied in manufacturing plants and received attention as well as application into production processes 1.2 Some robotic application 1.2.1 Application in industrial 1.2.2 Applications in laboratory 1.2.3 Application in nuclear technology 1.2.4 Application in agriculture 1.2.5 Application in space exploring 1.2.6 Application in submersible survey equipment CHAPTER SIMULATING PREFERENTIAL MOTION OF MOBILE ROBOTIC ARM AND DESIGNING NEW LAW OF VISUAL SERVOING FOLLING FLYING TARGET 2.2 Simulating preferential motion of camera on robotic arm and designing visual servo system following flying target 2.2.1 Description of coordinates 5 Y4 Camera XC YC ZC X4 Z0 Trục tilt Y3 Z3 Trục Pan Y0 Z4 X3 4 O0 X0 Figure 2.5 One two-free-grade robotic arm mounted with camera on a mobile robot with wheel The homogeneous matrix shows the position and direction of OCXCYCZC in O0X0Y0Z given for the following formula:  s34 c TC   34   c34 s5 c34c5 xM  xc  x x y x z x p x   s34 s5 s34c5 y M  yc  x y y y z y p y    c5 s5 hT  zc   x z yz zz pz  0   0  (2.1) 2.2.2 Preferential motion Jacobian matrix for robot has the following formula:   s34  c s  34 c c J   34     c34  s34 s5 s34 c5 0 0 0 c5 s5 0  0  1 0   0 0 c5 s5 (2.26) 2.2.3 Calculating the derivative of image characteristics Jacobi matrix of image characteristics   z J im   c  0   zc u zc v  zc uv u2   v2   uv       v    u   We have the formula to calculate the derivative of image characteristics as follows ξ  Jim J.θ  ζ (2.36) 2.2.4 Designing the Control Rule visual servoing folloing flying target - + Kinetic control (2.39) e Kinetic v d Chuyển động không xác định - + controll (2.43)  Chuyển động không xác định mục bay 2-DOF robotic arm with camera v Figure 2.11- Diagram of proposed visual servoing controller following flying target 2.2.4.2 Kinetic Control Rule    v  ξ  A      s5  ψ 5   u  (2.37) ψ describes the variation of image characteristic deviation due to indefinite motion of the flying target ψ can be estimated as following [16]:  pre   v  ˆ   pre - A  4pre  -   s5 4pre 5  -u  (2.38) With ψˆ is the estimated vector of ψ Furthermore,  pre ,4pre , and 5pre are the updated discrete data for ξ ,  , and  respectively We can choose the desired angular velocity for pan-pilt joints as    4d   1 ˆ following:    A   N  n    ,  5d    (2.39) T T Replacing  5  in (2.37) by  4d 5d  in (2.39), we have the following equation:    N  n  v   ,   s5 4d     u  (2.40) ˆ với ψ = ψ - ψ 2.2.4.3 Kinetic Control Rule Kinetic model for pan/pilt platform/ base is shown as following:   H  q  v  h  q, v  v  g  q  , (2.41) T T with q  4 5  , v   5  , τ   ,  ,  is the torque at pan joint,  is the torque at tilt joint (see Figure 2.9) All H  q  , h  q, v  and T g  q  are shown specifically in simulating parameters In order to design for kinetic control rule, the torque vector is chosen as following: τ  Γe  H  q  v d  h  q, v  v d  g q  , (2.43) T with v d   4d 5d  , e  v  v d Γ is the constant matrix, positive diagonal line can be chosen 2.2.5 Results of simulation -3 -4 x 10 truc V (m) huong cua chuyen dong -2 -4 quy dao dac trung anh toa (m) x 10 -0.5 -4 truc U (m) x 10 Figure 2.13 u v 0.5 -1 thoi gian (s) a) The trajectory moves of the image characteristics in the Sai lech van toc goc (rad/s) image plane b) Characteristics of coordinates per time -1   -2 -3  0.5 thoi gian (s) 1.5 13 thi toa cac khop toa khop (rad) 1.5 0.5 khop khop -0.5 -1 -1.5 thoi gian (s) 10 Figure 3.11 Diagram of joint angles Sai lech van toc khop Pan-Tilt -1 -2 e1=q1-qd1 -3 e2=q2-qd2 -4 Time (s) 10 Figure 3.12 Diagram for errors in joint velocity 3.2.5 Conclusion on the proposed control method In this chapter, the author has presented a method of building visual servoing system following the target The simulation results on Matlab show that the algorithm given is convergence with high accuracy Experimental studies on DPerception's actual use of robot models will be implemented in the near future Research directions for the robot-camera system placed on mobile or ship vehicles are being studied with the help of inertial blocks in the problem of platform stability 14 (*) Main contents in this chapter shall be published at the scientific work no [4] Nguyễn Tiến Kiệm, Pham Thuong Cat , „Velocity control for pantilt platform with camera following mobile target with uncertain parameters‟ , 6th Conference on mechatrocnics nationwide VCM2012, Hanoi dated on 14-15/12/2012, page 787-794 CHAPTER CONTROL ALGORITHMS FOR INDUSTRIAL ROBOT USING ARTIFICIAL NEURON NETWORK WITH ATTENTION TO THE ACTUATOR 4.2 Controlling robotic camera system following mobile target with attention to the impact of the actuator The control task is performed through the difference function between the desired image characteristic ξ d  const and the image characteristic obtained This deviation function can be defined as follows: e = (ξ - ξ ) d Control Rule Engine Ro bot Came Figure 4.5 Control diagram xc and xo respectively is the camera coordinates and target coordinates in the Cartesian coordinate system associated with the robot 15 platform The kinetic equation of the robot is described by the following equation: xc  p  q  (4.8) The derivative per time (4.8), we get: xc  p q  Jrq q t The kinetic equation of robot and actuator are described as follows: τ  H  q  q  h  q,q  (4.9) Li  Ri  Kq  t E  u E (4.10) τ = KT i  ˆ GJˆ K T R 1u E  H  1  ˆ GJˆ zH  1  ˆ  hˆ  K R 1Kq  GJq T ˆ GJˆ K T R 1Li  (H  GJ )q  H  ˆ GJ ˆ ψ = RK T1H       1 (4.25) GJq  h  R 1t E 1 ˆ GJˆ f1  RKT1 (H  GJ )q  H  ˆ GJ ˆ γ = RK T1 -H  1 (4.26) 1 GJq  h   K T1t E  Li  ˆ h ˆ   Kq GJq  (4.27) (4.28) Combining the equations (4.25), (4.26), (4.27), (4.28), we obtain the following new equation: ψz  γ  f1  uE 4.2.3 Control following mobile target using neuron network 16 uE  u0  u1 u0  ψ  K D z  K P z   γ u1 is the control signal to compensate for the uncertain component, which will be defined later Replace (4.30), (4.31) in (4.29) we get: z  K D z  K P z  ψ 1 u1  f1  Theory 4.1: The robotic system Pan Tilt-camera with two-free-grade has many uncertain parameters (4.29) with neural networks (4.38), (4.39) will follow moving targets with errors e  if we choose the control algorithm u and W of the network neuron as follows: u  ψ  K D z  K P z   γ  u1  s  u1   1   Wσ    s    W  sσT (4.41) (4.42) (4.43) In which KD = D + C, KP = DC; D is positive sysmmetric matrix D = D > 0,  ,   T 4.2.4 Simulation result of visual servo system with engine model on Matlab 17 DO THI DAC TRUNG ANH CUA CAMERA u[m] 0.2 0.15 0.1 0.05 -0.05 -0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0.01 v[m] Figure 4.7 Diagram of image characteristics q[rad] DO THI TOA DO KHOP CUA PAN TILT 1.5 0.5 q1 q2 -0.5 -1 -1.5 10 12 14 16 t[sec ] Figure 4.8: Diagram of joint coordinates DO THI VAN TOC KHOP PAN TILT q1 dot [rad/s] q2 dot -2 -4 -6 10 12 Figure 4.9: Diagream of robotic joint velocity 14 16 t[sec] 18 uE [V] DO THI DIEN AP CUA DONG CO TREN KHOP PAN TILT DIEN AP KHOP DIEN AP KHOP -1 -2 -3 -4 10 12 14 16 t [sec] Figure 4.10: Voltage diagram of engine on robotic joints The robot motor voltage control system - the camera is controlled to following the object, meeting the requirement of following target when there are many uncertainties in the kinetics of the Pan / Tilt platform We see in Figure 4.8 and 4.9 after a time of about 1.5 seconds basically the platform has stick to the target The error of the controlled system following the target for image characteristics in the center of the image has achieved high accuracy 4.2.5 Conclusion of the proposed control method In the main content of this chapter the author has presented the method of building a DC motor control algorithm for visual servoing system following target Simulation results on Matlab show that the algorithm given is convergence and high accuracy Experimental studies on actual models using DPerception pan / tilt platform will be deployed in the near future The research directions for pan / tilt platform standing on mobile or ship vehicles are being studied with the help of inertial blocks in the problem of platform stability 19 (*) Main content of the proposal is published in the scientific work no.[1] Nguyen Tien Kiem, Pham Thuong Cat, “Conrol of robot-camera system with actuator’s dynamic to tract moving object”, Informatics and Control Journals V.31, N.3(2015), tr 255-265 CHAPTER NON-LINEAR ADAPTIVE SLIDING CONTROL AGAINST THE DEGENERATION FOR ROBOTIC CAMERA WITH UNCERTAIN MODEL AND EXTERNAL NOISE 5.3 Kinetic model for fixed n-DOF armed robotics Kinetic model for this armed robotic as following [58] H  q  q  h  q, q  q  g  q   τd  τ, (5.1) with q, q, q  R n respectively are vectors of position, speed and velocity for joints H  q  presents inertial matrix h  q, q  is the Coriolis radial matrix g  q  the vector of gravity components τ d the limited vector for the total uncertainties including the uncertainty of the model as well as the external noise τ is the torque vector, which is considered the control input Characteristics 1: H  q  is reversible, positive and blocked matrix: H1 θ  θT H  q  θ  H θ , with θ  R in which H1 , H are positive, real and known constant 2 n Characteristics 2: H  q   2h  q, q  is the unaligned symmetry matrix On the other hand, we can rewrite n θT  H  q   2h  q, q  θ  0, with every θ  R 5.4 Designing control rule (5.3) 20 Control rule is proposed as following:    ˆ  Γsig  s   d ˆ, τ  fˆ x, W (5.20) In which dˆ is the aforementioned sustainable component and be specified   ˆ is the output of RBFNN and is applied to estimate f  x  , also later, fˆ x, W ˆ the estimated value of W and can be updated online by online weight W  ˆ is expressed as adjustment algorithmIn particular, the expression fˆ x, W  follows:    ˆ W ˆ Tσ  x  (5.21) fˆ x, W Then (5.7), (5.20), and (5.21) into (5.17) we have  H  q  s  h  q, q  s  WTσ  d  Γsig  s   dˆ , (5.22) ˆ In which d  ε  τd , W  W  W Next, the proposed online weight adjustment algorithm as follows : ˆ  HσsT , (5.23) W With H is the positive definite matrix and can be chosen Theory 1: Consider the n-DOF robotic arm described by (5.1) (Suppose 5.1) is satisfied If applicable for nonlinear sliding surfaces, control rules, online weighting adjustment algorithms, sustainable components and the sustainability factor online law proposed in (5.8), (5.20), (5.23), (5.25), and (5.26) respectively, all signals in the closed-loop control system are blocked, furthermore, the adhesion error converges to in the finite time 21 u RBFNN _ - e Sliding surface s + Control Armd robotics Sustainable component Figure 5.2 Diagram for the whole closed-loop control system 5.6 Simulation for control method Figure 5.3 Cling performance of the proposed TSMC method 22 Figure 5.4 Cling performance of the linear SMC method tien trinh bien thien e1 ca hai phuong phap TSMC duoc de xuat SMC tuyen tinh sai lech bam e1 (rad) Sai lech bam vi tri e1 (rad) -1 -2 thoi gian (s) x 10 TSMC duoc de xuat SMC tuyen tinh -2 -4 -6 -8 e1 trang thai xac lap -3 thoi gian (s) 10 12 Figure 5.5 Comparing in a steady state between the coupling error at coupling of the TSMC proposed method and SMC method Tien trinh cua e2 ca phuong phap sai lech bam e2 (rad) sai lech bam e2 (rad) -0.5 -1 TSMC duoc de xuat SMC tuyen tinh x 10 -4 -5 -10 TSMC duoc de xuat SMC tuyen tinh -1.5 thoi gian (s) -15 e2 gian doan xac lap thoi gian (s) 10 12 Figure 5.6 Comparing in the steady state between the error at the coupling of the TSMC proposed method and the linear SMC method Mo men khop phuong phap mo men quay (N.m) TSMC duoc de xuat SMC tuyen tinh 100 50 -50 mo men quay (N.m) Mo men khop ca phuong phap 150 TSMC duoc de xuat SMC tuyen tinh 100 50 -100 thoi gian (s) 10 12 thoi gian (s) 10 12 23 Figure 5.7 Comparison between control inputs at both coupling between TSMC proposed method and linear SMC method x 10 gian doan xac lap -3 phuong phap duoc de xuat phuong phap [58] sai lech bam e1 (rad) sai lech bam e1 o khop (rad) So sanh e1 phuong phap -1 -1 phuong phap duoc de xuat phuong phap [58] -2 -2 thoi gian (s) thoi gian (s) Figure 5.8 Comparing in the wrong steady state e1 at coupling between the So sanh e2 x 10 sai lech bam e2 (rad) sai lech bam e2 tai khop (rad) proposed method and the internal method [58] -0.5 -1 Phuong phap duoc de xuat phuong phap [58] thoi gian (s) phuong phap duoc de xuat phuong phap [58] -1 -1.5 giai doan xac lap -4 thoi gian (s) Hình 5.9 So sánh trạng thái ổn định sai lệch bám e2 khớp nối phương pháp đề xuất [58] Figure 5.10 Comparing the torque of the proposed method and [58] 24 Tai khop Tai khop 100 50 -50 -100 -150 Khong xu ly chattering co xu ly chattering thoi gian (s) Mo men quay (N.m) Mo men quay (N.m) 100 50 -50 -100 -150 khong xu ly chattering co xu ly chattering thoi gian (s) Figure 5.11 Comparison of torque in the case of use (5.25, 5.26) and smooth function (5.41, 5.42) so sanh hieu nang xu ly chattering (rad) x 10 giai doan xac lap -5 e1 khong xu ly chattering e1 khong xu ly chattering -2 2.5 3.5 4.5 5.5 thoi gian (s) 6.5 7.5 Figure 5.12 Compare the error of sticking at joint 1, in the case of using functions (5.25, 5.26) and using smooth functions (5.41, 5.42) 5.7 Conclusion on proposed control method In this section, the author has presented the method of TSMC to solve the problem of degeneration for fixed robot arms In addition to reducing some of the disadvantages of linear SMC method such as the bid for large torque control in instantaneous state but getting quite large error in steady state, TSMC proposed method still at full protection against the model uncertainty as well as external noise Furthermore, degenerative problems are also completely treated by the formula (4.66) Thanks to the 25 advantages and simplicity of this proposed TSMC method, it will be a good candidate for practical applications (*) Main contents for the proposal is published at the scientific work no.[3] Kiem NGUYEN, Tinh NGUYEN, Quyen BUI, Minhtuan PHAM, “Adaptive anti-singularity terminal sliding mode control for a robotic arm with model uncertainties and external disturbances”, Turkish journal of electrical engineering & computer sciences, E-ISSN: 1303-6203, ISSN: 1300-0632, DOI: 10.3906/elk-1711-137, Year:2018 Volume: 26 Number:6, page 3224-3238, tạp chí thuộc danh mục SCIE, IF: 0.58 CONCLUSION FOR THE DISSERTATIONThe dissertation has researched and developed control algorithms for pan-tilt-camera system placed on mobile robotics with many uncertain parameters Control method for pan-tilt-camera system following target with attention to the actuator with many uncertain parameters using artificial neural networks and nonlinear sliding control methods combined with artificial neural networks to control robotic arms with irregular patterns, external noise and resist degradation Control methods demonstrate the stability according to Lyapunov and LaSalle stability theory and are verified by Matlab simulation software The results of the dissertation The dissertation has four main contributions as following: - Simulating differential motion of robots and flying targets, studying and developing algorithms to control the robot-camera system placed on mobile robotic wheels to follow moving target with the uncertainty of robotic wheel and unknown flying target 26 - Researching and developing an algorithm to control robot-camera system with many uncertain parameters using artificial neural network with control signal as the joint torque - Researching and developing the algorithm to control the robot-camera system with attention to motors controlling the joints with many uncertain parameters of the kinematic model and of the electric motor - Researching and developing an algorithm to control industrial robot arm with uncertainty of dynamic model, external noise, prevent degeneration using adaptive sliding controller in combination with artificial neural network Development direction of the dissertation - Continueing to research and develop a control method for both mobile robots and robotic camera systems in considering the inconsistency, including uncertainties of wheel slip, uncertainty model, influence consideration of friction and external noise is blocked - Studying the control method for robot-camera to pay attention to the actuator structure of the wheel such as left-wheel motor control signal, gear motor must pay attention to uncertainties such as slip, tissue Uncertainty, external noise - Developing an experimental system to verify the proposed control methods LIST OF PUBLISHED SCIENTIFIC WORKS [1] Nguyen Tien Kiem, Pham Thuong Cat, “conrol of robot-camera system with actuator’s dynamic to tract moving object”, Informatics and control journals V.31, N.3(2015), tr 255-265 27 [2] Nguyen Tien Kiem, Hoang Thi Thuong, Nguyen Van Tinh, “Modeling the differential motion of a mobile manipulator and designing a new visual servoing for tracking a flying target”, Informatics and control journals V.33, N.4 (2017), tr 339-355 [3] Kiem NGUYEN, Tinh NGUYEN, Quyen BUI, Minhtuan PHAM, “Adaptive anti-singularity terminal sliding mode control for a robotic arm with model uncertainties and external disturbances”, Turkish journal of electrical engineering & computer sciences, E-ISSN: 1303-6203, ISSN: 1300-0632, DOI: 10.3906/elk-1711-137, Year:2018 Volume: 26 Number:6, page 3224-3238, journals under the list of SCIE, IF: 0.58 [4].Nguyen Tien Kiem, Pham Thuong Cat , „Speed control pan-tiltcamera platform following the moving targets with uncertain parameters’ , 6th Conference on mechatronics nationwide VCM2012, Hanoi dated on 1415/12/2012, page 787-794 [5].Nguyen Tien Kiem, Pham Thuong Cat, Nguyen Van Tinh „Robotic camera control following mobile target with attention to the impacts of the actuator‟, 2nd Conference on control and automation nationwide VCCA2013, Da Nang dated on 22-23/11/2013, page 321-327 [6] Nguyen Tien Kiem, Pham Thuong Cat , „Robotic camera control following mobile target with attention to impact of the actuator and LuGre dynamic friction model‟, 7th Conference on mechatronics VCM2014, Dong Nai, dated on 21-22/11/2014, page 506-513 [7] Nguyen Tien Kiem, „Robotic control system with attention to the impact of the unknown sub-loading and LuGre dynamic friction model‟ – 8th Conference on mechatronics VCM2016, Can Tho, dated on 2526/11/2016, page 802-805 ... with fixed n-DOF 19 5.4 Designing control law 19 5.6 Simulating control method 21 5.7 Conclusion on proposed control method 24 CONCLUSION OF THE DISSERTATION 25... The dissertation is defensed at the Council of Doctoral Dissertation Evaluation - Graduate Universty level at Vietnam Academy Science and Technology at … on date … month ….year 2011 The dissertation. .. necessity of the dissertation Controlling robot is still problematic due to the complexity, the nonlinearity and the uncertainty of the dynamical and kinetic equations caused by robots Recently the controlling