Biorobotics 7 / Mbed 2 deprecated Inverse_kinematic

Inverse kinematics

Dependencies:   Matrix mbed

main.cpp@2:8632e61cafc8, 2018-10-30 (annotated)

Committer:
MAHCSnijders
Date:
Tue Oct 30 13:36:23 2018 +0000
Revision:
2:8632e61cafc8
Parent:
1:df3d7f71db4b
Child:
3:f0208237b6f7
Final (zonder matrices)

Who changed what in which revision?

UserRevisionLine numberNew contents of line
MAHCSnijders 0:4a9c733c3b53 1 #include "mbed.h"
MAHCSnijders 0:4a9c733c3b53 2 #include "math.h"
MAHCSnijders 0:4a9c733c3b53 3
MAHCSnijders 1:df3d7f71db4b 4 const float L0 = 0.15; // Length between two motors [meter]
MAHCSnijders 1:df3d7f71db4b 5 const float L1 = 0.10; // Length first beam from right motor2 [meter]
MAHCSnijders 1:df3d7f71db4b 6 const float L2 = 0.30; // Length second beam from right motor2 [meter]
MAHCSnijders 1:df3d7f71db4b 7 const float L3 = 0.15; // Length beam between L2 and L4 [meter]
MAHCSnijders 1:df3d7f71db4b 8 const float L4 = 0.30; // Length first beam from left motor1 [meter]
MAHCSnijders 1:df3d7f71db4b 9 const float L5 = 0.35; // Length from L3 to end-effector [meter]
MAHCSnijders 0:4a9c733c3b53 10 const double PI = 3.14159265359;
MAHCSnijders 1:df3d7f71db4b 11 volatile float Pe_x; // x-coordinate of end-effector from frame 0 [meter]
MAHCSnijders 1:df3d7f71db4b 12 volatile float Pe_y; // y-coordinate of end-effector from frame 0 [meter]
MAHCSnijders 1:df3d7f71db4b 13 volatile static float des_motor_angle1; // Desired angle of motor 1 (left) based on kinematics [rad]
MAHCSnijders 1:df3d7f71db4b 14 volatile static float des_motor_angle2; // Desired angle of motor 2 (right) based on kinematics [rad]
MAHCSnijders 0:4a9c733c3b53 15
MAHCSnijders 1:df3d7f71db4b 16 Ticker kinematics_ticker; // Ticker function for inverse kinematics
MAHCSnijders 0:4a9c733c3b53 17
MAHCSnijders 0:4a9c733c3b53 18 void InverseKinematics()
MAHCSnijders 0:4a9c733c3b53 19 {
MAHCSnijders 0:4a9c733c3b53 20 // Calculation of the position of joint 3 in frame 0
MAHCSnijders 1:df3d7f71db4b 21 float n = sqrt(pow(Pe_x,2) + pow(Pe_y,2)); // Radius between origin frame 0 and endeffector [meter]
MAHCSnijders 0:4a9c733c3b53 22 float omega = acos(-(pow(n,2) - pow(L4,2) - pow(L5,2))/(2*L4*L5)); // Angle between L4 and L5 [rad]
MAHCSnijders 0:4a9c733c3b53 23 float q4 = PI - omega; // Angle of joint 3 between L3 and L4
MAHCSnijders 1:df3d7f71db4b 24 float theta = atan(L5*sin(q4)/(L4 + L5*cos(q4))); // Angle between n and L4
MAHCSnijders 0:4a9c733c3b53 25 float lambda = PI - atan(abs(Pe_y/Pe_x)); // Entire angle between x-axis frame 0 and n
MAHCSnijders 1:df3d7f71db4b 26 float des_motor_angle1 = lambda - theta;
MAHCSnijders 1:df3d7f71db4b 27 float J3x_0 = L4*cos(des_motor_angle1); // x-coordinate of joint 3 in frame 0
MAHCSnijders 1:df3d7f71db4b 28 float J3y_0 = L4*sin(des_motor_angle1); // y-coordinate of joint 3 in frame 0
MAHCSnijders 0:4a9c733c3b53 29
MAHCSnijders 0:4a9c733c3b53 30 // Calculation of the position of joint 2 in frame 0
MAHCSnijders 0:4a9c733c3b53 31 float S = abs(J3y_0 - Pe_y); // Distance between height endeffector and joint 3
MAHCSnijders 0:4a9c733c3b53 32 float kappa = asin(S/L5); // Angle of L5
MAHCSnijders 0:4a9c733c3b53 33 float J2x_0 = (L3+L5)*cos(kappa) + Pe_x; // x-coordinate of joint 2 in frame 0
MAHCSnijders 0:4a9c733c3b53 34 float J2y_0 = (L3+L5)*sin(kappa) + Pe_y; // y-coordinate of joint 2 in frame 0
MAHCSnijders 0:4a9c733c3b53 35
MAHCSnijders 0:4a9c733c3b53 36 // Calculation of the position of joint 1 in frame 0
MAHCSnijders 0:4a9c733c3b53 37 float J2x_1 = J2x_0 - L0; // x-coordinate of joint 2 in frame 1
MAHCSnijders 0:4a9c733c3b53 38 float J2y_1 = J2y_0; // y-coordinate of joint 2 in frame 1
MAHCSnijders 1:df3d7f71db4b 39 float r = sqrt(pow(J2x_1,2) + pow(J2y_1,2)); // Radius between origin frame 1 and J2
MAHCSnijders 1:df3d7f71db4b 40 float alfa = acos( -(pow(r,2) - pow(L1,2) - pow(L2,2))/(2*L1*L2) ); // Angle opposite of radius r
MAHCSnijders 0:4a9c733c3b53 41 float q2 = PI - alfa; // Angle between L1 and L2
MAHCSnijders 0:4a9c733c3b53 42
MAHCSnijders 0:4a9c733c3b53 43 // Calculation of motor_angle2
MAHCSnijders 0:4a9c733c3b53 44 float beta = atan(L2*sin(q2)/(L1+L2*cos(q2))); // Angle between r and L1
MAHCSnijders 1:df3d7f71db4b 45 float gamma = PI - atan(abs(J2y_1/J2x_1)); // Angle between r and x-axis
MAHCSnijders 0:4a9c733c3b53 46 // check if gamma works!
MAHCSnijders 1:df3d7f71db4b 47 des_motor_angle2 = gamma - beta;
MAHCSnijders 1:df3d7f71db4b 48 float J1x_0 = L0 + L1*cos(des_motor_angle2); // x-coordinate of joint 1 in frame 0
MAHCSnijders 1:df3d7f71db4b 49 float J1y_0 = L1*sin(des_motor_angle2); // y-coordinate of joint 1 in frame 0
MAHCSnijders 0:4a9c733c3b53 50
MAHCSnijders 1:df3d7f71db4b 51
MAHCSnijders 1:df3d7f71db4b 52 // Determining angle delta for safety
MAHCSnijders 1:df3d7f71db4b 53 float m = sqrt(pow((abs(J3x_0)+J1x_0),2) + pow((J3y_0 - J1y_0),2)); // Radius between Joint 1 and Joint 3
MAHCSnijders 1:df3d7f71db4b 54 float delta = acos(- (pow(m,2) - pow(L2,2) - pow(L3,2))/(2*L2*L3)); // Angle between L2 and L3
MAHCSnijders 1:df3d7f71db4b 55
MAHCSnijders 0:4a9c733c3b53 56 }
MAHCSnijders 0:4a9c733c3b53 57
MAHCSnijders 0:4a9c733c3b53 58
MAHCSnijders 0:4a9c733c3b53 59 int main()
MAHCSnijders 0:4a9c733c3b53 60 {
MAHCSnijders 1:df3d7f71db4b 61 kinematics_ticker.attach(InverseKinematics,0.5);
MAHCSnijders 0:4a9c733c3b53 62 }