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@ -2304,28 +2304,87 @@ bool Planner::_populate_block(block_t * const block, bool split_move, |
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const float junction_acceleration = limit_value_by_axis_maximum(block->acceleration, junction_unit_vec), |
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sin_theta_d2 = SQRT(0.5f * (1.0f - junction_cos_theta)); // Trig half angle identity. Always positive.
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vmax_junction_sqr = (junction_acceleration * junction_deviation_mm * sin_theta_d2) / (1.0f - sin_theta_d2); |
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vmax_junction_sqr = JUNC_SQ(junction_acceleration, sin_theta_d2); |
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if (block->millimeters < 1) { |
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// Fast acos approximation (max. error +-0.033 rads)
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// Based on MinMax polynomial published by W. Randolph Franklin, see
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// https://wrf.ecse.rpi.edu/Research/Short_Notes/arcsin/onlyelem.html
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// (acos(x) = pi / 2 - asin(x))
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const float neg = junction_cos_theta < 0 ? -1 : 1, |
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t = neg * junction_cos_theta, |
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asinx = 0.032843707f |
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+ t * (-1.451838349f |
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+ t * ( 29.66153956f |
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+ t * (-131.1123477f |
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+ t * ( 262.8130562f |
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+ t * (-242.7199627f + t * 84.31466202f) )))), |
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junction_theta = RADIANS(90) - neg * asinx; |
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t = neg * junction_cos_theta; |
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// If angle is greater than 135 degrees (octagon), find speed for approximate arc
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if (junction_theta > RADIANS(135)) { |
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// NOTE: MinMax acos approximation and thereby also junction_theta top out at pi-0.033, which avoids division by 0
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const float limit_sqr = block->millimeters / (RADIANS(180) - junction_theta) * junction_acceleration; |
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if (t < -0.7071067812f) { |
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#if ENABLED(JD_USE_MATH_ACOS) |
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#error "TODO: Inline maths with the MCU / FPU." |
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#elif ENABLED(JD_USE_LOOKUP_TABLE) |
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// Fast acos approximation (max. error +-0.01 rads)
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// Based on LUT table and linear interpolation
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/**
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* // Generate the JD Lookup Table
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* constexpr float c = 1.00751317f; // Correction factor to center error around 0
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* for (int i = 0; i < jd_lut_count - 1; ++i) { |
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* const float x0 = (sq(i) - 1) / sq(i), |
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* y0 = acos(x0) * (i ? c : 1), |
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* x1 = 0.5 * x0 + 0.5, |
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* y1 = acos(x1) * c; |
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* jd_lut_k[i] = (y0 - y1) / (x0 - x1); |
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* jd_lut_b[i] = (y1 * x0 - y0 * x1) / (x0 - x1); |
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* } |
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* jd_lut_k[jd_lut_count - 1] = jd_lut_b[jd_lut_count - 1] = 0; |
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* |
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* // Compute correction factor (Set c to 1.0f first!)
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* float min = INFINITY, max = -min; |
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* for (float t = 0; t <= 1; t += 0.0003f) { |
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* const float e = acos(t) / approx(t); |
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* if (isfinite(e)) { |
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* NOMORE(min, e); |
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* NOLESS(max, e); |
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* } |
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* } |
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* fprintf(stderr, "%.9gf, ", (min + max) / 2); |
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*/ |
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static constexpr int16_t jd_lut_count = 15; |
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static constexpr uint16_t jd_lut_tll = 1 << jd_lut_count; |
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static constexpr int16_t jd_lut_tll0 = __builtin_clz(jd_lut_tll) + 1; // i.e., 16 - jd_lut_count
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static constexpr float jd_lut_k[jd_lut_count] PROGMEM = { |
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-1.03146219f, -1.30760407f, -1.75205469f, -2.41705418f, -3.37768555f, |
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-4.74888229f, -6.69648552f, -9.45659828f, -13.3640289f, -18.8927879f, |
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-26.7136307f, -37.7754059f, -53.4200745f, -75.5457306f, 0.0f }; |
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static constexpr float jd_lut_b[jd_lut_count] PROGMEM = { |
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1.57079637f, 1.70886743f, 2.04220533f, 2.62408018f, 3.52467203f, |
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4.85301876f, 6.77019119f, 9.50873947f, 13.4009094f, 18.9188652f, |
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26.7320709f, 37.7884521f, 53.4292908f, 75.5522461f, 0.0f }; |
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const int16_t idx = (t == 0.0f) ? 0 : __builtin_clz(int16_t((1.0f - t) * jd_lut_tll)) - jd_lut_tll0; |
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float junction_theta = t * pgm_read_float(&jd_lut_k[idx]) + pgm_read_float(&jd_lut_b[idx]); |
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if (neg > 0) junction_theta = RADIANS(180) - junction_theta; |
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#else |
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// Fast acos(-t) approximation (max. error +-0.033rad = 1.89°)
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// Based on MinMax polynomial published by W. Randolph Franklin, see
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// https://wrf.ecse.rpi.edu/Research/Short_Notes/arcsin/onlyelem.html
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// acos( t) = pi / 2 - asin(x)
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// acos(-t) = pi - acos(t) ... pi / 2 + asin(x)
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const float asinx = 0.032843707f |
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+ t * (-1.451838349f |
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+ t * ( 29.66153956f |
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+ t * (-131.1123477f |
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+ t * ( 262.8130562f |
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+ t * (-242.7199627f |
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+ t * ( 84.31466202f ) ))))), |
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junction_theta = RADIANS(90) + neg * asinx; // acos(-t)
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// NOTE: junction_theta bottoms out at 0.033 which avoids divide by 0.
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#endif |
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const float limit_sqr = (block->millimeters * junction_acceleration) / junction_theta; |
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NOMORE(vmax_junction_sqr, limit_sqr); |
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} |
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} |
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@ -2363,11 +2422,10 @@ bool Planner::_populate_block(block_t * const block, bool split_move, |
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// Start with a safe speed (from which the machine may halt to stop immediately).
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float safe_speed = nominal_speed; |
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#ifdef TRAVEL_EXTRA_XYJERK |
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const float extra_xyjerk = (de <= 0) ? TRAVEL_EXTRA_XYJERK : 0; |
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#else |
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constexpr float extra_xyjerk = 0; |
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#ifndef TRAVEL_EXTRA_XYJERK |
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#define TRAVEL_EXTRA_XYJERK 0 |
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#endif |
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const float extra_xyjerk = (de <= 0) ? TRAVEL_EXTRA_XYJERK : 0; |
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uint8_t limited = 0; |
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TERN(HAS_LINEAR_E_JERK, LOOP_XYZ, LOOP_XYZE)(i) { |
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Štěpán Dalecký
5 years ago
GitHub