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Diffstat (limited to 'klippy/delta.py')
| -rw-r--r-- | klippy/delta.py | 310 |
1 files changed, 310 insertions, 0 deletions
diff --git a/klippy/delta.py b/klippy/delta.py new file mode 100644 index 00000000..0fa8caf2 --- /dev/null +++ b/klippy/delta.py @@ -0,0 +1,310 @@ +# Code for handling the kinematics of linear delta robots +# +# Copyright (C) 2016 Kevin O'Connor <kevin@koconnor.net> +# +# This file may be distributed under the terms of the GNU GPLv3 license. +import math, logging +import stepper, homing + +StepList = (0, 1, 2) + +class DeltaKinematics: + def __init__(self, printer, config): + steppers = ['stepper_a', 'stepper_b', 'stepper_c'] + self.steppers = [stepper.PrinterStepper(printer, config.getsection(n)) + for n in steppers] + radius = config.getfloat('delta_radius') + arm_length = config.getfloat('delta_arm_length') + self.arm_length2 = arm_length**2 + self.max_xy2 = min(radius, arm_length - radius)**2 + self.limit_xy2 = -1. + tower_height_at_zeros = math.sqrt(self.arm_length2 - radius**2) + self.max_z = self.steppers[0].position_max + self.limit_z = self.max_z - (arm_length - tower_height_at_zeros) + sin = lambda angle: math.sin(math.radians(angle)) + cos = lambda angle: math.cos(math.radians(angle)) + self.towers = [ + (cos(210.)*radius, sin(210.)*radius), + (cos(330.)*radius, sin(330.)*radius), + (cos(90.)*radius, sin(90.)*radius)] + self.stepper_pos = self.cartesian_to_actuator([0., 0., 0.]) + def build_config(self): + for stepper in self.steppers: + stepper.set_max_jerk(0.005 * stepper.max_accel) # XXX + for stepper in self.steppers: + stepper.build_config() + def get_max_speed(self): + # XXX - this returns conservative values + max_xy_speed = min(s.max_velocity for s in self.steppers) + max_xy_accel = min(s.max_accel for s in self.steppers) + return max_xy_speed, max_xy_accel + def cartesian_to_actuator(self, coord): + return [int((math.sqrt(self.arm_length2 + - (self.towers[i][0] - coord[0])**2 + - (self.towers[i][1] - coord[1])**2) + coord[2]) + * self.steppers[i].inv_step_dist + 0.5) + for i in StepList] + def actuator_to_cartesian(self, pos): + # Based on code from Smoothieware + tower1 = list(self.towers[0]) + [pos[0]] + tower2 = list(self.towers[1]) + [pos[1]] + tower3 = list(self.towers[2]) + [pos[2]] + + s12 = matrix_sub(tower1, tower2) + s23 = matrix_sub(tower2, tower3) + s13 = matrix_sub(tower1, tower3) + + normal = matrix_cross(s12, s23) + + magsq_s12 = matrix_magsq(s12) + magsq_s23 = matrix_magsq(s23) + magsq_s13 = matrix_magsq(s13) + + inv_nmag_sq = 1.0 / matrix_magsq(normal) + q = 0.5 * inv_nmag_sq + + a = q * magsq_s23 * matrix_dot(s12, s13) + b = -q * magsq_s13 * matrix_dot(s12, s23) # negate because we use s12 instead of s21 + c = q * magsq_s12 * matrix_dot(s13, s23) + + circumcenter = [tower1[0] * a + tower2[0] * b + tower3[0] * c, + tower1[1] * a + tower2[1] * b + tower3[1] * c, + tower1[2] * a + tower2[2] * b + tower3[2] * c] + + r_sq = 0.5 * q * magsq_s12 * magsq_s23 * magsq_s13 + dist = math.sqrt(inv_nmag_sq * (self.arm_length2 - r_sq)) + + return matrix_sub(circumcenter, matrix_mul(normal, dist)) + def set_position(self, newpos): + self.stepper_pos = self.cartesian_to_actuator(newpos) + def get_homed_position(self): + pos = [(self.stepper_pos[i] + self.steppers[i].get_homed_offset()) + * self.steppers[i].step_dist + for i in StepList] + return self.actuator_to_cartesian(pos) + def home(self, toolhead, axes): + # All axes are homed simultaneously + homing_state = homing.Homing(toolhead, [0, 1, 2]) + s = self.steppers[0] # Assume homing parameters same for all steppers + self.limit_xy2 = self.max_xy2 + # Initial homing + homepos = [0., 0., s.position_endstop, None] + coord = list(homepos) + coord[2] -= 1.5*(s.position_endstop) + homing_state.plan_home(list(coord), homepos, self.steppers + , s.homing_speed) + # Retract + coord[2] = homepos[2] - s.homing_retract_dist + homing_state.plan_move(list(coord), s.homing_speed) + # Home again + coord[2] -= s.homing_retract_dist + homing_state.plan_home(list(coord), homepos, self.steppers + , s.homing_speed/2.0) + return homing_state + def motor_off(self, move_time): + self.limit_xy2 = -1. + for stepper in self.steppers: + stepper.motor_enable(move_time, 0) + def query_endstops(self, move_time): + return homing.QueryEndstops(["a", "b", "c"], self.steppers) + def check_move(self, move): + end_pos = move.end_pos + xy2 = end_pos[0]**2 + end_pos[1]**2 + if xy2 > self.limit_xy2 or end_pos[2] < 0.: + if self.limit_xy2 < 0.: + raise homing.EndstopError(end_pos, "Must home first") + raise homing.EndstopError(end_pos) + if end_pos[2] > self.limit_z: + if end_pos[2] > self.max_z or xy2 > (self.max_z - end_pos[2])**2: + raise homing.EndstopError(end_pos) + def move_z(self, move_time, move): + if not move.axes_d[2]: + return + inv_accel = 1. / move.accel + inv_cruise_v = 1. / move.cruise_v + for i in StepList: + towerx_d = self.towers[i][0] - move.start_pos[0] + towery_d = self.towers[i][1] - move.start_pos[1] + tower_d2 = towerx_d**2 + towery_d**2 + height = math.sqrt(self.arm_length2 - tower_d2) + move.start_pos[2] + + mcu_time, so = self.steppers[i].prep_move(move_time) + inv_step_dist = self.steppers[i].inv_step_dist + step_dist = self.steppers[i].step_dist + steps = move.axes_d[2] * inv_step_dist + + step_pos = self.stepper_pos[i] + step_offset = step_pos - height * inv_step_dist + + # Acceleration steps + accel_multiplier = 2.0 * step_dist * inv_accel + if move.accel_r: + #t = sqrt(2*pos/accel + (start_v/accel)**2) - start_v/accel + accel_time_offset = move.start_v * inv_accel + accel_sqrt_offset = accel_time_offset**2 + accel_steps = move.accel_r * steps + count = so.step_sqrt( + mcu_time - accel_time_offset, accel_steps, step_offset + , accel_sqrt_offset, accel_multiplier) + step_pos += count + step_offset += count - accel_steps + mcu_time += move.accel_t + # Cruising steps + if move.cruise_r: + #t = pos/cruise_v + cruise_multiplier = step_dist * inv_cruise_v + cruise_steps = move.cruise_r * steps + count = so.step_factor( + mcu_time, cruise_steps, step_offset, cruise_multiplier) + step_pos += count + step_offset += count - cruise_steps + mcu_time += move.cruise_t + # Deceleration steps + if move.decel_r: + #t = cruise_v/accel - sqrt((cruise_v/accel)**2 - 2*pos/accel) + decel_time_offset = move.cruise_v * inv_accel + decel_sqrt_offset = decel_time_offset**2 + decel_steps = move.decel_r * steps + count = so.step_sqrt( + mcu_time + decel_time_offset, decel_steps, step_offset + , decel_sqrt_offset, -accel_multiplier) + step_pos += count + self.stepper_pos[i] = step_pos + def move(self, move_time, move): + axes_d = move.axes_d + if not axes_d[0] and not axes_d[1]: + self.move_z(move_time, move) + return + move_d = move.move_d + movez_r = 0. + inv_movexy_d = 1. / move_d + inv_movexy_r = 1. + if axes_d[2]: + movez_r = axes_d[2] * inv_movexy_d + inv_movexy_d = 1. / math.sqrt(axes_d[0]**2 + axes_d[1]**2) + inv_movexy_r = move_d * inv_movexy_d + + origx, origy, origz = move.start_pos[:3] + + accel_t = move.accel_t + cruise_end_t = accel_t + move.cruise_t + accel_d = move.accel_r * move_d + cruise_end_d = accel_d + move.cruise_r * move_d + + inv_cruise_v = 1. / move.cruise_v + inv_accel = 1. / move.accel + accel_time_offset = move.start_v * inv_accel + accel_multiplier = 2.0 * inv_accel + accel_offset = move.start_v**2 * 0.5 * inv_accel + decel_time_offset = move.cruise_v * inv_accel + cruise_end_t + decel_offset = move.cruise_v**2 * 0.5 * inv_accel + cruise_end_d + + for i in StepList: + # Find point on line of movement closest to tower + towerx_d = self.towers[i][0] - origx + towery_d = self.towers[i][1] - origy + closestxy_d = (towerx_d*axes_d[0] + towery_d*axes_d[1])*inv_movexy_d + tangentxy_d2 = towerx_d**2 + towery_d**2 - closestxy_d**2 + closest_height2 = self.arm_length2 - tangentxy_d2 + closest_height = math.sqrt(closest_height2) + closest_d = closestxy_d * inv_movexy_r + closestz = origz + closest_d*movez_r + + # Calculate accel/cruise/decel portions of move + reverse_d = closest_d + closest_height*movez_r*inv_movexy_r + accel_up_d = cruise_up_d = decel_up_d = 0. + accel_down_d = cruise_down_d = decel_down_d = 0. + if reverse_d <= 0.: + accel_down_d = accel_d + cruise_down_d = cruise_end_d + decel_down_d = move_d + elif reverse_d >= move_d: + accel_up_d = accel_d + cruise_up_d = cruise_end_d + decel_up_d = move_d + elif reverse_d < accel_d: + accel_up_d = reverse_d + accel_down_d = accel_d + cruise_down_d = cruise_end_d + decel_down_d = move_d + elif reverse_d < cruise_end_d: + accel_up_d = accel_d + cruise_up_d = reverse_d + cruise_down_d = cruise_end_d + decel_down_d = move_d + else: + accel_up_d = accel_d + cruise_up_d = cruise_end_d + decel_up_d = reverse_d + decel_down_d = move_d + + # Generate steps + inv_step_dist = self.steppers[i].inv_step_dist + step_dist = self.steppers[i].step_dist + step_pos = self.stepper_pos[i] + height = step_pos*step_dist - closestz + mcu_time, so = self.steppers[i].prep_move(move_time) + if accel_up_d > 0.: + count = so.step_delta_accel( + mcu_time - accel_time_offset, closest_d - accel_up_d, + step_dist, closest_d + accel_offset, + closest_height2, height, movez_r, accel_multiplier) + step_pos += count + height += count * step_dist + if cruise_up_d > 0.: + count = so.step_delta_const( + mcu_time + accel_t, closest_d - cruise_up_d, + step_dist, closest_d - accel_d, + closest_height2, height, movez_r, inv_cruise_v) + step_pos += count + height += count * step_dist + if decel_up_d > 0.: + count = so.step_delta_accel( + mcu_time + decel_time_offset, closest_d - decel_up_d, + step_dist, closest_d - decel_offset, + closest_height2, height, movez_r, -accel_multiplier) + step_pos += count + height += count * step_dist + if accel_down_d > 0.: + count = so.step_delta_accel( + mcu_time - accel_time_offset, closest_d - accel_down_d, + -step_dist, closest_d + accel_offset, + closest_height2, height, movez_r, accel_multiplier) + step_pos += count + height += count * step_dist + if cruise_down_d > 0.: + count = so.step_delta_const( + mcu_time + accel_t, closest_d - cruise_down_d, + -step_dist, closest_d - accel_d, + closest_height2, height, movez_r, inv_cruise_v) + step_pos += count + height += count * step_dist + if decel_down_d > 0.: + count = so.step_delta_accel( + mcu_time + decel_time_offset, closest_d - decel_down_d, + -step_dist, closest_d - decel_offset, + closest_height2, height, movez_r, -accel_multiplier) + step_pos += count + self.stepper_pos[i] = step_pos + + +###################################################################### +# Matrix helper functions for 3x1 matrices +###################################################################### + +def matrix_cross(m1, m2): + return [m1[1] * m2[2] - m1[2] * m2[1], + m1[2] * m2[0] - m1[0] * m2[2], + m1[0] * m2[1] - m1[1] * m2[0]] + +def matrix_dot(m1, m2): + return m1[0] * m2[0] + m1[1] * m2[1] + m1[2] * m2[2] + +def matrix_magsq(m1): + return m1[0]**2 + m1[1]**2 + m1[2]**2 + +def matrix_sub(m1, m2): + return [m1[0] - m2[0], m1[1] - m2[1], m1[2] - m2[2]] + +def matrix_mul(m1, s): + return [m1[0]*s, m1[1]*s, m1[2]*s] |