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