Biorobotics 7 / Mbed 2 deprecated Inverse_kinematic

Inverse kinematics

Dependencies:   Matrix mbed

main.cpp@3:f0208237b6f7, 2018-10-30 (annotated)

Committer:
MAHCSnijders
Date:
Tue Oct 30 19:51:44 2018 +0000
Revision:
3:f0208237b6f7
Parent:
2:8632e61cafc8
Child:
4:9f389b393af2
Final version with new frame 0

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 3:f0208237b6f7 10 const float L6 = 1.00; // Length from frame 0 to motor 1
MAHCSnijders 0:4a9c733c3b53 11 const double PI = 3.14159265359;
MAHCSnijders 1:df3d7f71db4b 12 volatile float Pe_x; // x-coordinate of end-effector from frame 0 [meter]
MAHCSnijders 1:df3d7f71db4b 13 volatile float Pe_y; // y-coordinate of end-effector from frame 0 [meter]
MAHCSnijders 1:df3d7f71db4b 14 volatile static float des_motor_angle1; // Desired angle of motor 1 (left) based on kinematics [rad]
MAHCSnijders 1:df3d7f71db4b 15 volatile static float des_motor_angle2; // Desired angle of motor 2 (right) based on kinematics [rad]
MAHCSnijders 0:4a9c733c3b53 16
MAHCSnijders 1:df3d7f71db4b 17 Ticker kinematics_ticker; // Ticker function for inverse kinematics
MAHCSnijders 0:4a9c733c3b53 18
MAHCSnijders 0:4a9c733c3b53 19 void InverseKinematics()
MAHCSnijders 0:4a9c733c3b53 20 {
MAHCSnijders 0:4a9c733c3b53 21 // Calculation of the position of joint 3 in frame 0
MAHCSnijders 3:f0208237b6f7 22 float n = sqrt(pow((L6-Pe_x),2) + pow(Pe_y,2)); // Radius between motor 1 and endeffector [meter]
MAHCSnijders 3:f0208237b6f7 23 float omega = acos(-(pow(n,2) - pow(L4,2) - pow(L5,2))/(2*L4*L5)); // Angle between L4 and L5 [rad]
MAHCSnijders 3:f0208237b6f7 24 float q4 = PI - omega; // Angle of joint 3 between L3 and L4
MAHCSnijders 3:f0208237b6f7 25 float theta = acos( -(pow(L5,2) - pow(n,2) - pow(L4,2))/(2*n*L4) ); // Angle between n and L4
MAHCSnijders 3:f0208237b6f7 26 float lambda = PI - atan(Pe_y/(L6-Pe_x)); // Entire angle between L0 and n
MAHCSnijders 3:f0208237b6f7 27 des_motor_angle1 = lambda - theta;
MAHCSnijders 3:f0208237b6f7 28 float J3x_0 = L6 + L4*cos(des_motor_angle1); // x-coordinate of joint 3 in frame 0
MAHCSnijders 3:f0208237b6f7 29 float J3y_0 = L4*sin(des_motor_angle1); // y-coordinate of joint 3 in frame 0
MAHCSnijders 0:4a9c733c3b53 30
MAHCSnijders 0:4a9c733c3b53 31 // Calculation of the position of joint 2 in frame 0
MAHCSnijders 3:f0208237b6f7 32 float S = abs(J3y_0 - Pe_y); // Distance between height endeffector and joint 3
MAHCSnijders 3:f0208237b6f7 33 float kappa = asin(S/L5); // Angle of L5
MAHCSnijders 3:f0208237b6f7 34 float J2x_0 = (L3+L5)*cos(kappa) + Pe_x; // x-coordinate of joint 2 in frame 0
MAHCSnijders 3:f0208237b6f7 35 float J2y_0 = (L3+L5)*sin(kappa) + Pe_y; // y-coordinate of joint 2 in frame 0
MAHCSnijders 0:4a9c733c3b53 36
MAHCSnijders 0:4a9c733c3b53 37 // Calculation of the position of joint 1 in frame 0
MAHCSnijders 3:f0208237b6f7 38 float J2x_1 = J2x_0 - L0 - L6; // x-coordinate of joint 2 in frame 1
MAHCSnijders 3:f0208237b6f7 39 float J2y_1 = J2y_0; // y-coordinate of joint 2 in frame 1
MAHCSnijders 3:f0208237b6f7 40 float r = sqrt(pow(J2x_1,2) + pow(J2y_1,2)); // Radius between origin frame 1 and J2
MAHCSnijders 3:f0208237b6f7 41 float alfa = acos( -(pow(r,2) - pow(L1,2) - pow(L2,2))/(2*L1*L2) ); // Angle opposite of radius r
MAHCSnijders 3:f0208237b6f7 42 float q2 = PI - alfa; // Angle between L1 and L2
MAHCSnijders 0:4a9c733c3b53 43
MAHCSnijders 0:4a9c733c3b53 44 // Calculation of motor_angle2
MAHCSnijders 3:f0208237b6f7 45 float beta = atan(L2*sin(q2)/(L1+L2*cos(q2))); // Angle between r and L1
MAHCSnijders 3:f0208237b6f7 46 float gamma = PI - atan(abs(J2y_1/J2x_1)); // Angle between r and x-axis
MAHCSnijders 0:4a9c733c3b53 47 // check if gamma works!
MAHCSnijders 1:df3d7f71db4b 48 des_motor_angle2 = gamma - beta;
MAHCSnijders 0:4a9c733c3b53 49
MAHCSnijders 1:df3d7f71db4b 50
MAHCSnijders 1:df3d7f71db4b 51 // Determining angle delta for safety
MAHCSnijders 3:f0208237b6f7 52 float J1x_0 = L0 + L6 + L1*cos(des_motor_angle2); // x-coordinate of joint 1 in frame 0
MAHCSnijders 3:f0208237b6f7 53 float J1y_0 = L1*sin(des_motor_angle2); // y-coordinate of joint 1 in frame 0
MAHCSnijders 3:f0208237b6f7 54
MAHCSnijders 3:f0208237b6f7 55 float m = sqrt(pow((J1x_0 - J3x_0),2) + pow((J3y_0 - J1y_0),2)); // Radius between Joint 1 and Joint 3
MAHCSnijders 3:f0208237b6f7 56 float delta = acos(- (pow(m,2) - pow(L2,2) - pow(L3,2))/(2*L2*L3)); // Angle between L2 and L3
MAHCSnijders 0:4a9c733c3b53 57 }
MAHCSnijders 0:4a9c733c3b53 58
MAHCSnijders 0:4a9c733c3b53 59
MAHCSnijders 0:4a9c733c3b53 60 int main()
MAHCSnijders 0:4a9c733c3b53 61 {
MAHCSnijders 1:df3d7f71db4b 62 kinematics_ticker.attach(InverseKinematics,0.5);
MAHCSnijders 0:4a9c733c3b53 63 }