linuxcnc-hal-sys 0.1.5

//
// This is a kinematics module for the Scorbot ER 3.
//
// Copyright (C) 2015-2016 Sebastian Kuzminsky <seb@highlab.com>
//
// This program is free software; you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 2 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program; if not, write to the Free Software
// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301 USA
//

//
// The origin of the G53 coordinate system is at the center of rotation of
// joint J0, and at the bottom of the base plate.
//
// FIXME: The origin should probably be at the bottom of the base (part 5
// in the parts diagram on page 7-11 of the SCORBOT-ER III User's Manual).
//
// Joint 0 is rotation around the Z axis.  It chooses the plane that
// the rest of the arm moves in.
//
// Joint 1 is the shoulder.
//
// Joint 2 is the elbow.
//
// Joint 3 is pitch of the wrist, joint 4 is roll of the wrist.  These are
// converted to motor actuations by an external differential comp in HAL.
//


#include "kinematics.h"
#include "rtapi_math.h"
#include "gotypes.h"


//
// linkage constants, in mm & degrees
//

// Link 0 connects the origin to J1 (shoulder)
// These dimensions come off a drawing I got from Intelitek.
#define L0_HORIZONTAL_DISTANCE 16
#define L0_VERTICAL_DISTANCE   140

#define L1_LENGTH 221  // Link 1 connects J1 (shoulder) to J2 (elbow)
#define L2_LENGTH 221  // Link 2 connects J2 (shoulder) to the wrist


// Compute the cartesian coordinates of J1, given the J0 angle (and the
// fixed, known link L0 between J0 and J1).
static void compute_j1_cartesian_location(double j0, EmcPose *j1_cart) {
    j1_cart->tran.x = L0_HORIZONTAL_DISTANCE * cos(TO_RAD * j0);
    j1_cart->tran.y =  L0_HORIZONTAL_DISTANCE * sin(TO_RAD * j0);
    j1_cart->tran.z = L0_VERTICAL_DISTANCE;
    j1_cart->a = 0;
    j1_cart->b = 0;
    j1_cart->c = 0;
    j1_cart->u = 0;
    j1_cart->v = 0;
    j1_cart->w = 0;
}


// Forward kinematics takes the joint positions and computes the cartesian
// coordinates of the controlled point.
int kinematicsForward(
    const double *joints,
    EmcPose *pose,
    const KINEMATICS_FORWARD_FLAGS *fflags,
    KINEMATICS_INVERSE_FLAGS *iflags
) {
    EmcPose j1_vector;  // the vector from j0 ("base") to joint 1 ("shoulder", end of link 0)
    EmcPose j2_vector;  // the vector from j1 ("shoulder") to  joint 2 ("elbow", end of link 1)
    EmcPose j3_vector;  // the vector from j2 ("elbow") to joint 3 ("wrist", end of link 2)

    double r;

    // rtapi_print("fwd: j0=%f, j1=%f, j2=%f\n", joints[0], joints[1], joints[2]);
    compute_j1_cartesian_location(joints[0], &j1_vector);
    // rtapi_print("fwd: j1=(%f, %f, %f)\n", j1_vector.tran.x, j1_vector.tran.y, j1_vector.tran.z);

    // Link 1 connects j1 (shoulder) to j2 (elbow).
    r = L1_LENGTH * cos(TO_RAD * joints[1]);
    j2_vector.tran.x = r * cos(TO_RAD * joints[0]);
    j2_vector.tran.y =  r * sin(TO_RAD * joints[0]);
    j2_vector.tran.z = L1_LENGTH * sin(TO_RAD * joints[1]);
    // rtapi_print("fwd: j2=(%f, %f, %f)\n", j2_vector.tran.x, j2_vector.tran.y, j2_vector.tran.z);

    // Link 2 connectes j2 (elbow) to j3 (wrist).
    // J3 is the controlled point.
    r = L2_LENGTH * cos(TO_RAD * joints[2]);
    j3_vector.tran.x = r * cos(TO_RAD * joints[0]);
    j3_vector.tran.y =  r * sin(TO_RAD * joints[0]);
    j3_vector.tran.z = L2_LENGTH * sin(TO_RAD * joints[2]);
    // rtapi_print("fwd: j3=(%f, %f, %f)\n", j3_vector.tran.x, j3_vector.tran.y, j3_vector.tran.z);

    // The end-effector location is the sum of the linkage vectors.
    pose->tran.x = j1_vector.tran.x + j2_vector.tran.x + j3_vector.tran.x;
    pose->tran.y = j1_vector.tran.y + j2_vector.tran.y + j3_vector.tran.y;
    pose->tran.z = j1_vector.tran.z + j2_vector.tran.z + j3_vector.tran.z;
    // rtapi_print("fwd: pose=(%f, %f, %f)\n", pose->tran.x, pose->tran.y, pose->tran.z);

    // A and B are wrist roll and pitch, handled in hal by external kinematics
    pose->a = joints[3];
    pose->b = joints[4];

    return 0;
}


//
// Inverse kinematics takes the cartesian coordinates of the controlled
// point and computes corresponding the joint positions.
//
// Joint 0 rotates the arm around the base.  The rest of the joints are
// confined to the vertical plane containing J0, and rotated around the
// vertical at J0.  This kinematics code calls this plane the "RZ" plane.
// The Z coordinate in this plane is the same as the Z coordinate in the
// "cartesian" coordinates of LinuxCNC's world space.  The R coordinate
// is the horizontal distance (ie, in the XY plane) of the controlled
// point from J0.
//
int kinematicsInverse(
    const EmcPose *pose,
    double *joints,
    const KINEMATICS_INVERSE_FLAGS *iflags,
    KINEMATICS_FORWARD_FLAGS *fflags
) {
    // EmcPose j1_cart;
    double distance_to_cp, distance_to_center;
    double r_j1, z_j1;   // (r_j1, z_j1) is the location of J1 in the RZ plane
    double r_cp, z_cp;   // (r_cp, z_cp) is the location of the controlled point in the RZ plane
    double angle_to_cp;
    double j1_angle;

    // the location of J2, this is what we're trying to find
    double z_j2;

    // rtapi_print("inv: x=%f, y=%f, z=%f\n", pose->tran.x, pose->tran.y, pose->tran.z);

    // J0 is easy.  Project the (X, Y, Z) of the pose onto the Z=0 plane.
    // J0 points at the projected (X, Y) point.  tan(J0) = Y/X
    // J0 then defines the plane that the rest of the arm operates in.
    joints[0] = TO_DEG * atan2(pose->tran.y, pose->tran.x);
    // rtapi_print("inv: j0=%f\n", joints[0]);

    // compute_j1_cartesian_location(joints[0], &j1_cart);
    // rtapi_print("inv: j1=(X=%f, Y=%f, Z=%f)\n", j1_cart.tran.x, j1_cart.tran.y, j1_cart.tran.z);

    // FIXME: Until i figure the wrist differential out, the controlled
    //     point will be the location of the wrist joint, J3/J4.

    // The location of J1 (computed above) and the location of the
    // controlled point are separated by J1, L1, J2, and L2.  L1 and L2 are
    // known, but J1 and J2 are not.

    // (r_j1, z_j1) is the location of J1 in the RZ plane (the vertical
    // plane defined by the angle of J0, with the origin at the location
    // of J0.  This is just a known, static vector.
    r_j1 = L0_HORIZONTAL_DISTANCE;
    z_j1 = L0_VERTICAL_DISTANCE;
    // rtapi_print("inv: r_j1=%f, z_j1=%f\n", r_j1, z_j1);

    // (r_cp, z_cp) is the location of J3 (the controlled point), again in
    // the plane defined by the angle of J0, with the origin of the
    // machine.
    r_cp = sqrt(pow(pose->tran.x, 2) +  pow(pose->tran.y, 2));
    z_cp = pose->tran.z;
    // rtapi_print("inv: r_cp=%f, z_cp=%f (controlled point)\n", r_cp, z_cp);

    // translate so (r_j1, z_j1) is the origin of the coordinate system
    r_cp -= r_j1;
    z_cp -= z_j1;
    // rtapi_print("inv: r_cp=%f, z_cp=%f (translated controlled point)\n", r_cp, z_cp);

    //
    // Now the origin (aka J1), J2, and CP define a triangle in the RZ plane.
    // The triangle is isosceles, because from the origin to J2 is L1, and
    // from J2 to CP is L2, and L1 and L2 are the same length.
    //
    // Bisect the base of that triangle, and call the center point of the
    // base "Center".
    //
    // Draw a line between J2 and Center.  This defines two right
    // triangles: (J1, J2, Center) and (CP, J2, Center).
    //
    // The length of the (J1, Center) and (CP, Center) lines are equal, and
    // are half the distance from the origin to CP.
    //

    distance_to_cp = sqrt(pow(r_cp, 2) + pow(z_cp, 2));
    distance_to_center = distance_to_cp / 2;
    // rtapi_print("inv: distance to cp: %f\n", distance_to_cp);

    // find the angle of the vector from the origin to the CP
    angle_to_cp = TO_DEG * acos(r_cp / distance_to_cp);
    if (z_cp < 0) {
        angle_to_cp *= -1;
    }
    // rtapi_print("inv: angle to cp: %f\n", angle_to_cp);

    // find the angle (Center, J1, J2)
    j1_angle = TO_DEG * acos(distance_to_center / L1_LENGTH);
    // rtapi_print("inv: j1 angle: %f\n", j1_angle);

    joints[1] = angle_to_cp + j1_angle;
    // rtapi_print("inv: j1: %f\n", joints[1]);

    // now we can compute the location of J2
    z_j2 = L1_LENGTH * sin(TO_RAD * joints[1]);
    // rtapi_print("inv: r_j2=%f, z_j2=%f (translated j2)\n", r_j2, z_j2);

    joints[2] = -1.0 * TO_DEG * asin((z_j2 - z_cp) / L2_LENGTH);


#if 0
    // Distance between controlled point and the location of j1.  These two
    // points are separated by link 1, joint 1, and link 2.
    distance_between_centers = sqrt(pow((r2 - r1), 2) + pow((z2 - z1), 2));

    if (distance_between_centers > (L1_LENGTH + L2_LENGTH)) {
        // trying to reach too far
        return GO_RESULT_RANGE_ERROR;
    }

    if (distance_between_centers < fabs(L1_LENGTH - L2_LENGTH)) {
        // trying to reach too far into armpit
        return GO_RESULT_RANGE_ERROR;
    }

    delta = (1.0 / 4.0) * sqrt((distance_between_centers + L1_LENGTH + L2_LENGTH) * (distance_between_centers + L1_LENGTH - L2_LENGTH) * (distance_between_centers - L1_LENGTH + L2_LENGTH) * (L1_LENGTH + L2_LENGTH - distance_between_centers));

    ir1 = ((r1 + r2) / 2) + (((r2 - r1) * (pow(L1_LENGTH, 2) - pow(L2_LENGTH, 2)))/(2 * pow(distance_between_centers, 2))) + ((2 * (z1 - z2) * delta) / pow(distance_between_centers, 2));
    ir2 = ((r1 + r2) / 2) + (((r2 - r1) * (pow(L1_LENGTH, 2) - pow(L2_LENGTH, 2)))/(2 * pow(distance_between_centers, 2))) - ((2 * (z1 - z2) * delta) / pow(distance_between_centers, 2));

    iz1 = ((z1 + z2) / 2) + (((z2 - z1) * (pow(L1_LENGTH, 2) - pow(L2_LENGTH, 2)))/(2 * pow(distance_between_centers, 2))) - ((2 * (r1 - r2) * delta) / pow(distance_between_centers, 2));
    iz2 = ((z1 + z2) / 2) + (((z2 - z1) * (pow(L1_LENGTH, 2) - pow(L2_LENGTH, 2)))/(2 * pow(distance_between_centers, 2))) + ((2 * (r1 - r2) * delta) / pow(distance_between_centers, 2));


    // (ir1, iz1) is one intersection point, (ir2, iz2) is the other.
    // These are the possible locations of the J2 joint.
    // FIXME: For now we arbitrarily pick the one with the bigger Z.

    if (iz1 > iz2) {
        j2_r = ir1;
        j2_z = iz1;
    } else {
        j2_r = ir2;
        j2_z = iz2;
    }
    // rtapi_print("inv: j2_r=%f, j2_z=%f (J2, intersection point)\n", j2_r, j2_z);

    // Make J1 point at J2 (j2_r, j2_z).
    {
        double l1_r = j2_r - r1;
        joints[1] = TO_DEG * acos(l1_r / L1_LENGTH);
        // rtapi_print("inv: l1_r=%f, j1=%f\n", l1_r, joints[1]);
    }

    // Make J2 point at the controlled point.
    {
        double l2_r = r2 - j2_r;
        double j2;
        j2 = TO_DEG * acos(l2_r / L2_LENGTH);
        if (j2_z > pose->tran.z) {
            j2 *= -1;
        }
        joints[2] = j2;
        // rtapi_print("inv: l2_r=%f, j2=%f\n", l2_r, joints[2]);
    }
#endif

    // A and B are wrist roll and pitch, handled in hal by external kinematics
    joints[3] = pose->a;
    joints[4] = pose->b;

    return 0;
}


KINEMATICS_TYPE kinematicsType(void) {
    return KINEMATICS_BOTH;
}


#include "rtapi.h"
#include "rtapi_app.h"
#include "hal.h"

EXPORT_SYMBOL(kinematicsType);
EXPORT_SYMBOL(kinematicsForward);
EXPORT_SYMBOL(kinematicsInverse);
MODULE_LICENSE("GPL");

static int comp_id;

int rtapi_app_main(void) {
    comp_id = hal_init("scorbot-kins");
    if (comp_id < 0) {
        return comp_id;
    }
    hal_ready(comp_id);
    return 0;
}

void rtapi_app_exit(void) {
    hal_exit(comp_id);
}