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PROFERIS - Mi³osz Stocki
2026-07-06 11:34:03 +02:00
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/**
* WijiBoard – Kinematics (exact port of PositionControl.cpp)
* web/js/kinematics.js
*
* ── Mechanism: symmetric 5-bar parallel linkage ─────────────────
*
* END EFFECTOR (x, y)
* / \
* L2 (110) L2 (110)
* / \
* ELBOW1 ELBOW2
* \ /
* L1 (85) L1 (85)
* \ /
* MOTOR1 (-d2,0) MOTOR2 (+d2,0)
* | |
* [===BASE===] (d=25.8 mm wide)
* d2=12.9 mm
*
* Both motors are mounted in the centre mechanism box.
* Motor 1 is at (-d2, 0), Motor 2 is at (+d2, 0).
* Each motor drives a proximal arm (l1). The distal arms (l2)
* connect the elbows to the shared end-effector.
*
* IK: given target (x, y), solve θ1 and θ2 independently:
* Motor 1 sees the target at (x - d2, y) from its pivot.
* Motor 2 sees the target at (x + d2, y) from its pivot.
* Each uses the standard 2-link IK (law of cosines).
*
* Source: lib/Position/PositionControl.cpp (nerd-sniped/WijiBoard)
*/
// ── Exact constants from PositionControl.cpp ─────────────────────
const ARM = {
d: 25.8, // full motor separation (mm)
d2: 12.9, // half motor separation — motor 1 at (-d2,0), motor 2 at (+d2,0)
l1: 85.0, // proximal link length (mm)
l2: 110.0, // distal link length (mm)
STEPS_PER_REV: 2048,
STEP_ANGLE_DEG: 360 / 2048, // ≈ 0.17578125°
};
// ── Workspace limits ──────────────────────────────────────────────
const LIMITS = {
// Outer bounding box (the board surface)
X_MIN: -150,
X_MAX: 150,
Y_MIN: -30, // numbers sit slightly below Y=0
Y_MAX: 145,
// Centre exclusion zone (the motor/mechanism box)
// Motors are at ±12.9 mm; box is a bit larger to account for the housing
BOX_HALF_W: 22, // ±22 mm in X (tune to real hardware)
BOX_HALF_H: 22, // 0..22 mm in Y (box sits above the base line)
BOX_Y_MIN: -5,
BOX_Y_MAX: 22,
};
// ── Letter / number position lookup table ────────────────────────
// Directly ported from PositionControl.cpp
const LOOKUP_TABLE = {
'Q': { x: -66.5, y: 91.6 },
'W': { x: 70.8, y: 92.0 },
'E': { x: -41.4, y: 125.5 },
'R': { x: -44.0, y: 96.0 },
'T': { x: 1.3, y: 97.8 },
'Y': { x: 117.8, y: 91.7 },
'U': { x: 22.5, y: 98.3 },
'I': { x: 53.5, y: 124.5 },
'O': { x: -112.0, y: 82.0 },
'P': { x: -90.0, y: 89.0 },
'A': { x: -143.0, y: 99.0 },
'S': { x: -19.8, y: 98.0 },
'D': { x: -68.5, y: 121.7 },
'F': { x: -19.5, y: 127.0 },
'G': { x: 4.0, y: 128.4 },
'H': { x: 31.3, y: 127.3 },
'J': { x: 72.5, y: 121.0 },
'K': { x: 93.0, y: 116.8 },
'L': { x: 114.3, y: 110.2 },
'Z': { x: 130.0, y: 75.0 },
'X': { x: 95.9, y: 87.3 },
'C': { x: -94.0, y: 116.0 },
'V': { x: 44.5, y: 97.0 },
'B': { x: -119.0, y: 109.0 },
'N': { x: -135.4, y: 75.1 },
'M': { x: 132.0, y: 100.5 },
'+': { x: -110.0, y: 1.0 },
'-': { x: 110.0, y: 1.0 },
'*': { x: 110.0, y: -24.0 },
',': { x: -110.0, y: -24.0 },
'0': { x: -130.4, y: 44.2 },
'1': { x: -101.1, y: 53.3 },
'2': { x: -71.5, y: 60.4 },
'3': { x: -41.7, y: 65.2 },
'4': { x: -13.0, y: 66.5 },
'5': { x: 16.3, y: 68.0 },
'6': { x: 45.8, y: 64.0 },
'7': { x: 75.7, y: 61.1 },
'8': { x: 103.6, y: 53.8 },
'9': { x: 132.1, y: 45.0 },
};
// ── IK solver — exact port of calculateInverseKinematics() ───────
/**
* Compute motor angles for a given target end-effector position.
* Exactly mirrors the C++ implementation in PositionControl.cpp.
*
* @param {number} x Target X in mm (origin = midpoint between motors)
* @param {number} y Target Y in mm
* @returns {{ theta1: number, theta2: number, reachable: boolean }}
* theta1 / theta2 in RADIANS (motor 1 = left, motor 2 = right)
*/
function solve(x, y) {
const { d2, l1, l2 } = ARM;
// ── Motor 1 (left pivot at -d2, 0) ───────────────────────────
const xmd = x - d2; // target X relative to left motor
const s = Math.sqrt(xmd * xmd + y * y); // distance: left motor → target
const cosW1 = (l2 * l2 - s * s - l1 * l1) / (-2 * l1 * s);
if (cosW1 < -1 || cosW1 > 1) return { theta1: 0, theta2: 0, reachable: false };
const q = Math.atan2(y, xmd);
const w1 = Math.acos(cosW1);
const theta1 = q - w1;
// ── Motor 2 (right pivot at +d2, 0) ──────────────────────────
const xpd = x + d2; // target X relative to right motor
const t = Math.sqrt(xpd * xpd + y * y); // distance: right motor → target
const cosW2 = (l2 * l2 - t * t - l1 * l1) / (-2 * l1 * t);
if (cosW2 < -1 || cosW2 > 1) return { theta1: 0, theta2: 0, reachable: false };
const r = Math.atan2(y, xpd);
const w2 = Math.acos(cosW2);
const theta2 = r + w2;
return { theta1, theta2, reachable: true };
}
// ── Forward kinematics ───────────────────────────────────────────
/**
* Given motor angles, compute elbow and end-effector positions.
* The end-effector is found as the intersection of the two distal
* link circles — this is the FK complement to the 5-bar IK above.
*
* In practice for visualisation we just re-derive the elbow
* positions from each motor.
*
* @param {number} theta1 Motor 1 angle (radians)
* @param {number} theta2 Motor 2 angle (radians)
* @returns {{
* elbow1: {x,y}, elbow2: {x,y},
* endX: number, endY: number
* }}
*/
function forward(theta1, theta2) {
const { d2, l1, l2 } = ARM;
// Elbow 1 (tip of motor 1's proximal link)
const e1x = -d2 + l1 * Math.cos(theta1);
const e1y = l1 * Math.sin(theta1);
// Elbow 2 (tip of motor 2's proximal link)
const e2x = d2 + l1 * Math.cos(theta2);
const e2y = l1 * Math.sin(theta2);
// End-effector: intersection of circle(elbow1, l2) and circle(elbow2, l2)
// Use the same approach as the IK: each distal link points from its elbow to the EE.
// For visualisation accuracy, reconstruct EE by reversing the IK:
// From IK: theta1 = q - w1 → q = atan2(y, x - d2)
// We know theta1 and the elbow position, so EE is at l2 along some direction.
// Simplest: use circle-circle intersection of the two elbow-radius-l2 circles.
const dx = e2x - e1x;
const dy = e2y - e1y;
const dist = Math.sqrt(dx * dx + dy * dy);
if (dist < 1e-6 || dist > 2 * l2) {
// Degenerate / unreachable — just average the two elbows
return {
elbow1: { x: e1x, y: e1y },
elbow2: { x: e2x, y: e2y },
endX: (e1x + e2x) / 2,
endY: (e1y + e2y) / 2,
};
}
const a = dist / 2;
const h = Math.sqrt(l2 * l2 - a * a);
const mx = (e1x + e2x) / 2;
const my = (e1y + e2y) / 2;
// Two intersection candidates — pick the one with higher Y (the "up" configuration)
const px1 = mx + h * (dy / dist);
const py1 = my - h * (dx / dist);
const px2 = mx - h * (dy / dist);
const py2 = my + h * (dx / dist);
const { endX, endY } = py1 > py2
? { endX: px1, endY: py1 }
: { endX: px2, endY: py2 };
return {
elbow1: { x: e1x, y: e1y },
elbow2: { x: e2x, y: e2y },
endX, endY,
};
}
// ── Workspace check ───────────────────────────────────────────────
/**
* Check whether a point is inside the valid workspace.
* @param {number} x
* @param {number} y
* @returns {{ ok: boolean, reason: string }}
*/
function checkWorkspace(x, y) {
// Outer bounding box
if (x < LIMITS.X_MIN || x > LIMITS.X_MAX)
return { ok: false, reason: `X=${x.toFixed(1)} outside board limits [${LIMITS.X_MIN}, ${LIMITS.X_MAX}]` };
if (y < LIMITS.Y_MIN || y > LIMITS.Y_MAX)
return { ok: false, reason: `Y=${y.toFixed(1)} outside board limits [${LIMITS.Y_MIN}, ${LIMITS.Y_MAX}]` };
// Centre exclusion zone (mechanism box)
if (
x > -LIMITS.BOX_HALF_W && x < LIMITS.BOX_HALF_W &&
y > LIMITS.BOX_Y_MIN && y < LIMITS.BOX_Y_MAX
) {
return { ok: false, reason: `(${x.toFixed(1)}, ${y.toFixed(1)}) is inside the mechanism exclusion zone` };
}
// IK reachability
const { reachable } = solve(x, y);
if (!reachable) return { ok: false, reason: `(${x.toFixed(1)}, ${y.toFixed(1)}) is outside arm reach` };
return { ok: true, reason: '' };
}
// ── Lookup ────────────────────────────────────────────────────────
function lookup(char) {
return LOOKUP_TABLE[char.toUpperCase()] ?? null;
}
// ── Unit converters ───────────────────────────────────────────────
function stepsToRad(steps) {
return (steps / ARM.STEPS_PER_REV) * 2 * Math.PI;
}
function radToSteps(rad) {
return Math.round((rad / (2 * Math.PI)) * ARM.STEPS_PER_REV);
}
function stepsToDeg(steps) {
return steps * ARM.STEP_ANGLE_DEG;
}
function radToDeg(rad) {
return rad * 180 / Math.PI;
}
export default {
ARM, LIMITS, LOOKUP_TABLE,
solve, forward, checkWorkspace, lookup,
stepsToRad, radToSteps, stepsToDeg, radToDeg,
};