Design and fabricate a humanoid robot and build the walk trajectory

Design and fabricate a humanoid robot and build the walk trajectory Le, Thanh Quanga a Department of Mechatronics, University of Technical Education of Ho Chi Minh City, VietNam, July, 2012 lequangthanh010290@hotmail.coma Abstract To be able to calculate and control a humanoid robot, one of the important problems is modeling the robot Modeling is establishing a system by using the performing mathematics, so that we will have the core awareness for solving Some other requirements are response times Forward and inverse kinematic equations for position and orientation use more Sin, Cosin, Arcsin, Arccos functions, which require more time to calculate In addition, we need to calculate the forward kinematics and inverse kinematics of the robot Solving the inverse kinematics is the basic and complex problems, because we not have the typical methods, they deal more with the number of degrees of freedom, positions and orientation of end points and the difficulty in solving the complex mathematical equations I Introductions This project will design the mechanical part, electrical part, software utility, design walk trajectory and control a robot to walk like this We need six degrees of freedom (DOF) to define one point or body in space,3 DOF of position and DOF for orientation, DOF of position are determined by using the coordinate system With x, y, z coordinate, DOF of orientation is described by rotary This report will determine how to model and resolve the forward and inverse kinematics base on Denavit - Hartenberg theory and adopt Levenberg-Marquardt theory about numeric matrix to solve forward and inverse kinematic equations for position and orientation angle around the coordinate axis There are some version of humanoid robot are built from the Ho Chi Minh City University of Technology, Viet Nam These versions have the advantages of using harmonic gearbox, which has the character of high ratio, error reduction at output, friction reduction at input DC servo motor enclosed with one encoder and one microchip These chips communicate together by using CAN network The disadvantages of them are: heavy weight, spend more time to calculate the trajectory directly So, we have the D-H tables for left and right foot # With modeling, they use translation matrixes and rotary matrixes to demonstrate the robot, and use analytic method for solving the inverse kinematics In this project, we will use DenavidHartenberg theory to model the robot and use numeric method for solving the inverse kinematics By using RC servo motor, this has light weight, easy to control… II L L12 L34 L45 L56 L67 L78 L89 d 0 L23 0 0 0 a 90 -90 90 0 -90 t 0 0 Ɵ4 Ɵ5 Ɵ6 Ɵ7 Ɵ8 Tab D-H table for left foot # Results and Discussion Modeling the robot: We need to show how many degrees of freedom the robot has? l L12 L10_11 L11_12 L12_13 L13_14 L14_15 L15_16 d 0 -L2_10 0 0 0 a 90 -90 90 0 -90 t 0 0 Ɵ11 Ɵ12 Ɵ13 Ɵ14 Ɵ15 Tab D-H table for right foot Denevit – Hartenberg theory:[1] Transposed matrix from N coordinate to N+1 coordinate: n Tn1 Cn,n 1  Sn,n 1 S Cn,n 1 n Tn 1   n,n 1  0   0 ln 1Cn,n 1  lnCn  ln 1Sn,n 1  ln Sn     Transposed matrix from R coordinate to H coordinate: R Fig Modeling of robot Figure indicates the typical modeling, in real robot we have some angles not rotate For walk trajectory, we will care of the position and orientation of hip and feet Forward kinematic: TH R T1.1T2 T3 k Tk 1 n1TH  A1.A2.A3 An R: Reference H: Hand of Robot From the transposed matrix from R coordinate to H coordinate:  nx n R TH   y  nz  0 ox oy ax ay oz az xA  y A  zA   1 Euler(Φ, Ɵ ,Ψ) = Rot(z,Φ) Rot(y,Ɵ) Rot(x,Ψ)= CC C   S S CC S  S C  CS  S C C   CS  S C S  CC  S S Euler(,  , )     S C  S S C  0  Ca Co  S C RPY(a , o , n )   a o   So   CaSoSn  SaCn SaSoS  CaCn CaSoCn  SaSn SaSoCn  CaSn CoSn CoCn Jacobi matrix: We have the position of end point: With a robot have mechanisms:  Px   x A  P    y   y  A  Pz   z A  Inverse kinematic: Position and orientation: Fig Two mechanisms robot Coordinate of B:  xB   L1 Cos(1 )  L2Cos(1  2 )   y    L Sin( )  L Sin(   )   B   1 2   Fig Position and orientation With the same position , but in above figure, the orientation of A is different We have the forward kinematic equation of position and orientation: Differentiating this equation with respect to the two variables Ɵ1, Ɵ2:  d xB   L1Sin1  L2 Sin(1  2 )  d1      d yB   L1Cos1 L2Cos(1  2 )  d2  We have Jacobi matrix: TH  T  Px , Py , Pz  RPY  Øa , Øo , Ø  n L1Sin1 R TH  T  Px , Py , Pz  Euler  Øa , Øo ,  n 1Cos1 ØL R  L2 Sin(1   )  L2Cos(1   )  0  0  1 0  0  1  d xB   d1      Jacobi      D   J  D  d yB  d2    D    J 1   D D  J D  D  J 1.D   1       J  X  x  D      D  X  x      J 1.x    J 1.e   n  J 1.e   n 1 If we have inverse Jacobi matrix, we will solve the inverse kinematics problem But Jacobi matrix is non-square matrix, we may not calculate it We attempt to find other method to solve it Levenberg-Marquardt has published one method to calculate the inverse matrix, which is not square matrix [2]   J T  JJ T   I  dX 1 Fig Algorithm of control Start Initializing of position and orientation:  x, y, z    x0 , y0 , z0   , ,   0 , ,  Design walk trajectory: In walking project, the orbit of hip and foot must be ensuring like a human So, we must design the trajectory for hip and foot At first we need to find one point, which does not change the position while walking The orbit of hip and foot are defined by the equation of order 3 x(t)= a.t + b.t + c.t + Calculate the errors: We need to design walk trajectory in e  f Oyz  f0 planes Oxy and set   J T  JJ T   I  e 1      Fig Chart of foot on zcoordinate Fig Trajectory of hip, foot on Oxy plane Fig 9.Chart of Hip on x coordinate Fig Trajectory of hip, foot on Oyz plane Fig 10 Chart of Hip on y coordinate Fig 6.Chart of foot on x coordinate Fig 6.Chart of Hip on coordinate Fig 7.Chart of foot on y coordinate Mechanism[3] To reach the accuracy in control, the mechanical design of robot is complex, difficult Material of robot is aluminum, using Solidwork software to design CAD model The RC servo motors were used Character of robot: name dimension Agrees of freedom weigh character 212x450x60 16 56g Tab D-H table for right foot Control: Use a computer to calculate the value for each step of walk project dspic 30f6014A chip to control these motors Dspic 30F6014A (Master) Fig 10 Full CAD model of robot Dspic 30F6014A (Slave) Servo Servo Servo Servo 10 Servo Servo 11 Servo Servo 12 Servo Servo 13 Servo Servo 14 Servo Servo 15 Servo Servo 16 Fig 12 Block of hardware Fig 11 Assembly of robot Fig 13 Electric hardware [4] Simulation and experiment Fig 14 Walking process in plane Fig 15 Walking process in plane Fig 16 Walking process in plane 3 11 12 13 14 15 16 17 18 10 19 Fig 17 Walking process in real III Conclusions: This project show the method to model, solve the forward and inverse kinematic equations of position and orientation Finding the way to calculate the inverse kinematic with orientation is so important There are so many robot uses the orientation in its act In painting robot, the hand of robot is always parallel with thing need to paint A serving robot handles a glass of water, which is not fallen out… The disadvantages of this project are: the trajectories were designed before update for chips permanently Because of low speed, these chips can not calculate the trajectory as online process while robot is walking The mechanism parts, electronic hardware were made by hand, the nonaccuracy motors had The flexibility of this method help us to develop the robot, which can go up stair, down stair, walk on non -plane surface References B.Niku, S., Introduction to Robotics Analysis, Systems, Applications, 2001: United States of America Gavin, H., The LevenbergMarquardt method for nonlinear least squares curve-fitting problems September 28,2011 CO LTD, K.K., Hardware manual KHR-1, K.K CO LTD, Editor Sep.2004 High-Performance, -.b and D.S Controllers, dsPIC30F6011A/6012A/6013A/601 4A Data Sheet, Mocrochip, Editor 2008  ... kinematic with orientation is so important There are so many robot uses the orientation in its act In painting robot, the hand of robot is always parallel with thing need to paint A serving robot. .. speed, these chips can not calculate the trajectory as online process while robot is walking The mechanism parts, electronic hardware were made by hand, the nonaccuracy motors had The flexibility...These chips communicate together by using CAN network The disadvantages of them are: heavy weight, spend more time to calculate the trajectory directly So, we have the D-H tables for left and