Biorobotics 7 / Mbed 2 deprecated Inverse_kinematic

Inverse kinematics

Dependencies:   Matrix mbed

main.cpp@4:9f389b393af2, 2018-10-31 (annotated)

Committer:
MAHCSnijders
Date:
Wed Oct 31 13:55:22 2018 +0000
Revision:
4:9f389b393af2
Parent:
3:f0208237b6f7
Child:
5:aaf68c7482bc
Inverse kinematics with safety checks

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 4:9f389b393af2 17 DigitalOut safetyLED(LED_BLUE); // Safety check LED
MAHCSnijders 4:9f389b393af2 18
MAHCSnijders 1:df3d7f71db4b 19 Ticker kinematics_ticker; // Ticker function for inverse kinematics
MAHCSnijders 0:4a9c733c3b53 20
MAHCSnijders 0:4a9c733c3b53 21 void InverseKinematics()
MAHCSnijders 0:4a9c733c3b53 22 {
MAHCSnijders 0:4a9c733c3b53 23 // Calculation of the position of joint 3 in frame 0
MAHCSnijders 3:f0208237b6f7 24 float n = sqrt(pow((L6-Pe_x),2) + pow(Pe_y,2)); // Radius between motor 1 and endeffector [meter]
MAHCSnijders 3:f0208237b6f7 25 float omega = acos(-(pow(n,2) - pow(L4,2) - pow(L5,2))/(2*L4*L5)); // Angle between L4 and L5 [rad]
MAHCSnijders 3:f0208237b6f7 26 float q4 = PI - omega; // Angle of joint 3 between L3 and L4
MAHCSnijders 3:f0208237b6f7 27 float theta = acos( -(pow(L5,2) - pow(n,2) - pow(L4,2))/(2*n*L4) ); // Angle between n and L4
MAHCSnijders 3:f0208237b6f7 28 float lambda = PI - atan(Pe_y/(L6-Pe_x)); // Entire angle between L0 and n
MAHCSnijders 3:f0208237b6f7 29 des_motor_angle1 = lambda - theta;
MAHCSnijders 3:f0208237b6f7 30 float J3x_0 = L6 + L4*cos(des_motor_angle1); // x-coordinate of joint 3 in frame 0
MAHCSnijders 3:f0208237b6f7 31 float J3y_0 = L4*sin(des_motor_angle1); // y-coordinate of joint 3 in frame 0
MAHCSnijders 0:4a9c733c3b53 32
MAHCSnijders 0:4a9c733c3b53 33 // Calculation of the position of joint 2 in frame 0
MAHCSnijders 3:f0208237b6f7 34 float S = abs(J3y_0 - Pe_y); // Distance between height endeffector and joint 3
MAHCSnijders 3:f0208237b6f7 35 float kappa = asin(S/L5); // Angle of L5
MAHCSnijders 3:f0208237b6f7 36 float J2x_0 = (L3+L5)*cos(kappa) + Pe_x; // x-coordinate of joint 2 in frame 0
MAHCSnijders 3:f0208237b6f7 37 float J2y_0 = (L3+L5)*sin(kappa) + Pe_y; // y-coordinate of joint 2 in frame 0
MAHCSnijders 0:4a9c733c3b53 38
MAHCSnijders 0:4a9c733c3b53 39 // Calculation of the position of joint 1 in frame 0
MAHCSnijders 3:f0208237b6f7 40 float J2x_1 = J2x_0 - L0 - L6; // x-coordinate of joint 2 in frame 1
MAHCSnijders 3:f0208237b6f7 41 float J2y_1 = J2y_0; // y-coordinate of joint 2 in frame 1
MAHCSnijders 3:f0208237b6f7 42 float r = sqrt(pow(J2x_1,2) + pow(J2y_1,2)); // Radius between origin frame 1 and J2
MAHCSnijders 3:f0208237b6f7 43 float alfa = acos( -(pow(r,2) - pow(L1,2) - pow(L2,2))/(2*L1*L2) ); // Angle opposite of radius r
MAHCSnijders 3:f0208237b6f7 44 float q2 = PI - alfa; // Angle between L1 and L2
MAHCSnijders 0:4a9c733c3b53 45
MAHCSnijders 0:4a9c733c3b53 46 // Calculation of motor_angle2
MAHCSnijders 3:f0208237b6f7 47 float beta = atan(L2*sin(q2)/(L1+L2*cos(q2))); // Angle between r and L1
MAHCSnijders 3:f0208237b6f7 48 float gamma = PI - atan(abs(J2y_1/J2x_1)); // Angle between r and x-axis
MAHCSnijders 0:4a9c733c3b53 49 // check if gamma works!
MAHCSnijders 1:df3d7f71db4b 50 des_motor_angle2 = gamma - beta;
MAHCSnijders 0:4a9c733c3b53 51
MAHCSnijders 1:df3d7f71db4b 52
MAHCSnijders 1:df3d7f71db4b 53 // Determining angle delta for safety
MAHCSnijders 3:f0208237b6f7 54 float J1x_0 = L0 + L6 + L1*cos(des_motor_angle2); // x-coordinate of joint 1 in frame 0
MAHCSnijders 3:f0208237b6f7 55 float J1y_0 = L1*sin(des_motor_angle2); // y-coordinate of joint 1 in frame 0
MAHCSnijders 3:f0208237b6f7 56
MAHCSnijders 3:f0208237b6f7 57 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 58 float delta = acos(- (pow(m,2) - pow(L2,2) - pow(L3,2))/(2*L2*L3)); // Angle between L2 and L3
MAHCSnijders 4:9f389b393af2 59
MAHCSnijders 4:9f389b393af2 60
MAHCSnijders 4:9f389b393af2 61 // Implementing stops for safety
MAHCSnijders 4:9f389b393af2 62 // 45 < Motor_angle1 < 70 graden
MAHCSnijders 4:9f389b393af2 63 if (0.785398 < des_motor_angle1 && des_motor_angle1 < 1.22173)
MAHCSnijders 4:9f389b393af2 64 {
MAHCSnijders 4:9f389b393af2 65 kinematics_ticker.detach();
MAHCSnijders 4:9f389b393af2 66 safetyLED = 0;
MAHCSnijders 4:9f389b393af2 67 }
MAHCSnijders 4:9f389b393af2 68
MAHCSnijders 4:9f389b393af2 69 // -42 < Motor_angle2 < 85 graden
MAHCSnijders 4:9f389b393af2 70 if (-0.733038 < des_motor_angle2 && des_motor_angle2 < 1.48353)
MAHCSnijders 4:9f389b393af2 71 {
MAHCSnijders 4:9f389b393af2 72 kinematics_ticker.detach();
MAHCSnijders 4:9f389b393af2 73 safetyLED = 0;
MAHCSnijders 4:9f389b393af2 74 }
MAHCSnijders 4:9f389b393af2 75
MAHCSnijders 4:9f389b393af2 76 // Delta < 170 graden
MAHCSnijders 4:9f389b393af2 77 if (delta < 2.96706)
MAHCSnijders 4:9f389b393af2 78 {
MAHCSnijders 4:9f389b393af2 79 kinematics_ticker.detach();
MAHCSnijders 4:9f389b393af2 80 safetyLED = 0;
MAHCSnijders 4:9f389b393af2 81 }
MAHCSnijders 0:4a9c733c3b53 82 }
MAHCSnijders 0:4a9c733c3b53 83
MAHCSnijders 0:4a9c733c3b53 84
MAHCSnijders 0:4a9c733c3b53 85 int main()
MAHCSnijders 0:4a9c733c3b53 86 {
MAHCSnijders 4:9f389b393af2 87 safetyLED = 1;
MAHCSnijders 4:9f389b393af2 88 while (true) {
MAHCSnijders 1:df3d7f71db4b 89 kinematics_ticker.attach(InverseKinematics,0.5);
MAHCSnijders 4:9f389b393af2 90 }
MAHCSnijders 0:4a9c733c3b53 91 }