298 lines
13 KiB
Python
298 lines
13 KiB
Python
# Code for handling the kinematics of linear delta robots
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#
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# Copyright (C) 2016 Kevin O'Connor <kevin@koconnor.net>
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#
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# This file may be distributed under the terms of the GNU GPLv3 license.
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import math, logging
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import stepper, homing
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StepList = (0, 1, 2)
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# Slow moves once the ratio of tower to XY movement exceeds SLOW_RATIO
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SLOW_RATIO = 3.
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class DeltaKinematics:
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def __init__(self, printer, config):
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self.config = config
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self.steppers = [stepper.PrinterStepper(
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printer, config.getsection('stepper_' + n), n)
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for n in ['a', 'b', 'c']]
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self.need_motor_enable = self.need_home = True
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self.max_velocity = self.max_z_velocity = 0.
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self.radius = radius = config.getfloat('delta_radius')
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arm_length = config.getfloat('delta_arm_length')
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self.arm_length2 = arm_length**2
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self.max_xy2 = min(radius, arm_length - radius)**2
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self.limit_xy2 = -1.
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tower_height_at_zeros = math.sqrt(self.arm_length2 - radius**2)
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self.max_z = self.steppers[0].position_max
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self.limit_z = self.max_z - (arm_length - tower_height_at_zeros)
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logging.info(
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"Delta max build height %.2fmm (radius tapered above %.2fmm)" % (
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self.max_z, self.limit_z))
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sin = lambda angle: math.sin(math.radians(angle))
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cos = lambda angle: math.cos(math.radians(angle))
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self.towers = [
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(cos(210.)*radius, sin(210.)*radius),
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(cos(330.)*radius, sin(330.)*radius),
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(cos(90.)*radius, sin(90.)*radius)]
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# Find the point where an XY move could result in excessive
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# tower movement
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half_min_step_dist = min([s.step_dist for s in self.steppers]) * .5
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dist = (SLOW_RATIO * math.sqrt(self.arm_length2 / (SLOW_RATIO**2 + 1.)
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- half_min_step_dist**2)
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+ half_min_step_dist)
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self.slow_xy2 = (dist - radius)**2
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logging.info(
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"Delta max build radius %.2fmm (moves slowed past %.2fmm)" % (
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math.sqrt(self.max_xy2), math.sqrt(self.slow_xy2)))
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def set_max_jerk(self, max_xy_halt_velocity, max_velocity, max_accel):
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self.max_velocity = max_velocity
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max_z_velocity = self.config.getfloat('max_z_velocity', max_velocity)
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self.max_z_velocity = min(max_velocity, max_z_velocity)
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for stepper in self.steppers:
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stepper.set_max_jerk(max_xy_halt_velocity, max_accel)
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def build_config(self):
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for stepper in self.steppers:
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stepper.build_config()
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self.set_position([0., 0., 0.])
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def _cartesian_to_actuator(self, coord):
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return [int((math.sqrt(self.arm_length2
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- (self.towers[i][0] - coord[0])**2
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- (self.towers[i][1] - coord[1])**2) + coord[2])
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* self.steppers[i].inv_step_dist + 0.5)
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for i in StepList]
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def _actuator_to_cartesian(self, pos):
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# Based on code from Smoothieware
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tower1 = list(self.towers[0]) + [pos[0]]
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tower2 = list(self.towers[1]) + [pos[1]]
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tower3 = list(self.towers[2]) + [pos[2]]
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s12 = matrix_sub(tower1, tower2)
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s23 = matrix_sub(tower2, tower3)
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s13 = matrix_sub(tower1, tower3)
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normal = matrix_cross(s12, s23)
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magsq_s12 = matrix_magsq(s12)
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magsq_s23 = matrix_magsq(s23)
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magsq_s13 = matrix_magsq(s13)
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inv_nmag_sq = 1.0 / matrix_magsq(normal)
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q = 0.5 * inv_nmag_sq
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a = q * magsq_s23 * matrix_dot(s12, s13)
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b = -q * magsq_s13 * matrix_dot(s12, s23) # negate because we use s12 instead of s21
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c = q * magsq_s12 * matrix_dot(s13, s23)
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circumcenter = [tower1[0] * a + tower2[0] * b + tower3[0] * c,
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tower1[1] * a + tower2[1] * b + tower3[1] * c,
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tower1[2] * a + tower2[2] * b + tower3[2] * c]
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r_sq = 0.5 * q * magsq_s12 * magsq_s23 * magsq_s13
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dist = math.sqrt(inv_nmag_sq * (self.arm_length2 - r_sq))
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return matrix_sub(circumcenter, matrix_mul(normal, dist))
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def set_position(self, newpos):
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pos = self._cartesian_to_actuator(newpos)
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for i in StepList:
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self.steppers[i].mcu_stepper.set_position(pos[i])
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self.limit_xy2 = -1.
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def home(self, homing_state):
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# All axes are homed simultaneously
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homing_state.set_axes([0, 1, 2])
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s = self.steppers[0] # Assume homing parameters same for all steppers
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self.need_home = False
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# Initial homing
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homepos = [0., 0., s.position_endstop, None]
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coord = list(homepos)
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coord[2] = -1.5 * math.sqrt(self.arm_length2-self.max_xy2)
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homing_state.home(list(coord), homepos, self.steppers, s.homing_speed)
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# Retract
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coord[2] = homepos[2] - s.homing_retract_dist
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homing_state.retract(list(coord), s.homing_speed)
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# Home again
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coord[2] -= s.homing_retract_dist
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homing_state.home(list(coord), homepos, self.steppers
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, s.homing_speed/2.0, second_home=True)
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# Set final homed position
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coord = [(s.mcu_stepper.commanded_position + s.get_homed_offset())
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* s.step_dist
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for s in self.steppers]
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homing_state.set_homed_position(self._actuator_to_cartesian(coord))
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def motor_off(self, move_time):
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self.limit_xy2 = -1.
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for stepper in self.steppers:
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stepper.motor_enable(move_time, 0)
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self.need_motor_enable = self.need_home = True
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def _check_motor_enable(self, move_time):
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for i in StepList:
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self.steppers[i].motor_enable(move_time, 1)
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self.need_motor_enable = False
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def query_endstops(self, print_time):
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endstops = [(s, s.query_endstop(print_time)) for s in self.steppers]
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return [(s.name, es.query_endstop_wait()) for s, es in endstops]
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def check_move(self, move):
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end_pos = move.end_pos
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xy2 = end_pos[0]**2 + end_pos[1]**2
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if xy2 <= self.limit_xy2 and not move.axes_d[2]:
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# Normal XY move
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return
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if self.need_home:
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raise homing.EndstopMoveError(end_pos, "Must home first")
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limit_xy2 = self.max_xy2
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if end_pos[2] > self.limit_z:
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limit_xy2 = min(limit_xy2, (self.max_z - end_pos[2])**2)
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if xy2 > limit_xy2 or end_pos[2] < 0. or end_pos[2] > self.max_z:
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raise homing.EndstopMoveError(end_pos)
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if move.axes_d[2]:
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move.limit_speed(self.max_z_velocity, move.accel)
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limit_xy2 = -1.
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# Limit the speed/accel of this move if is is at the extreme
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# end of the build envelope
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extreme_xy2 = max(xy2, move.start_pos[0]**2 + move.start_pos[1]**2)
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if extreme_xy2 > self.slow_xy2:
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min_step = min([s.step_dist for s in self.steppers])
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d = math.sqrt(extreme_xy2) + self.radius
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r = SLOW_RATIO * min_step / (
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math.sqrt(self.arm_length2 - (d - min_step)**2)
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- math.sqrt(self.arm_length2 - d**2))
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max_velocity = self.max_velocity
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if move.axes_d[2]:
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max_velocity = self.max_z_velocity
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move.limit_speed(max_velocity * r, move.accel * r)
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limit_xy2 = -1.
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self.limit_xy2 = min(limit_xy2, self.slow_xy2)
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def move(self, move_time, move):
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axes_d = move.axes_d
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move_d = movexy_d = move.move_d
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movexy_r = 1.
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movez_r = 0.
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inv_movexy_d = 1. / movexy_d
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if not axes_d[0] and not axes_d[1]:
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movez_r = axes_d[2] * inv_movexy_d
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movexy_d = movexy_r = inv_movexy_d = 0.
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elif axes_d[2]:
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movexy_d = math.sqrt(axes_d[0]**2 + axes_d[1]**2)
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movexy_r = movexy_d * inv_movexy_d
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movez_r = axes_d[2] * inv_movexy_d
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inv_movexy_d = 1. / movexy_d
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if self.need_motor_enable:
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self._check_motor_enable(move_time)
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origx, origy, origz = move.start_pos[:3]
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accel_t = move.accel_t
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cruise_end_t = accel_t + move.cruise_t
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accel_d = move.accel_r * move_d
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cruise_end_d = accel_d + move.cruise_r * move_d
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inv_cruise_v = 1. / move.cruise_v
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inv_accel = 1. / move.accel
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accel_time_offset = move.start_v * inv_accel
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accel_multiplier = 2.0 * inv_accel
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accel_offset = move.start_v**2 * 0.5 * inv_accel
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decel_time_offset = move.cruise_v * inv_accel + cruise_end_t
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decel_offset = move.cruise_v**2 * 0.5 * inv_accel + cruise_end_d
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for i in StepList:
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# Find point on line of movement closest to tower
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towerx_d = self.towers[i][0] - origx
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towery_d = self.towers[i][1] - origy
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closestxy_d = (towerx_d*axes_d[0] + towery_d*axes_d[1])*inv_movexy_d
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tangentxy_d2 = towerx_d**2 + towery_d**2 - closestxy_d**2
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closest_height2 = self.arm_length2 - tangentxy_d2
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# Calculate accel/cruise/decel portions of move
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reversexy_d = closestxy_d + math.sqrt(closest_height2)*movez_r
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accel_up_d = cruise_up_d = decel_up_d = 0.
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accel_down_d = cruise_down_d = decel_down_d = 0.
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if reversexy_d <= 0.:
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accel_down_d = accel_d
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cruise_down_d = cruise_end_d
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decel_down_d = move_d
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elif reversexy_d >= movexy_d:
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accel_up_d = accel_d
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cruise_up_d = cruise_end_d
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decel_up_d = move_d
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elif reversexy_d < accel_d * movexy_r:
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accel_up_d = reversexy_d * move_d * inv_movexy_d
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accel_down_d = accel_d
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cruise_down_d = cruise_end_d
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decel_down_d = move_d
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elif reversexy_d < cruise_end_d * movexy_r:
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accel_up_d = accel_d
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cruise_up_d = reversexy_d * move_d * inv_movexy_d
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cruise_down_d = cruise_end_d
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decel_down_d = move_d
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else:
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accel_up_d = accel_d
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cruise_up_d = cruise_end_d
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decel_up_d = reversexy_d * move_d * inv_movexy_d
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decel_down_d = move_d
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# Generate steps
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mcu_stepper = self.steppers[i].mcu_stepper
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mcu_time = mcu_stepper.print_to_mcu_time(move_time)
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step_pos = mcu_stepper.commanded_position
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step_dist = self.steppers[i].step_dist
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height = step_pos*step_dist - origz
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if accel_up_d > 0.:
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count = mcu_stepper.step_delta_accel(
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mcu_time - accel_time_offset, accel_up_d,
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accel_offset, accel_multiplier, step_dist,
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height, closestxy_d, closest_height2, movez_r)
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height += count * step_dist
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if cruise_up_d > 0.:
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count = mcu_stepper.step_delta_const(
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mcu_time + accel_t, cruise_up_d,
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-accel_d, inv_cruise_v, step_dist,
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height, closestxy_d, closest_height2, movez_r)
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height += count * step_dist
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if decel_up_d > 0.:
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count = mcu_stepper.step_delta_accel(
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mcu_time + decel_time_offset, decel_up_d,
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-decel_offset, -accel_multiplier, step_dist,
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height, closestxy_d, closest_height2, movez_r)
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height += count * step_dist
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if accel_down_d > 0.:
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count = mcu_stepper.step_delta_accel(
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mcu_time - accel_time_offset, accel_down_d,
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accel_offset, accel_multiplier, -step_dist,
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height, closestxy_d, closest_height2, movez_r)
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height += count * step_dist
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if cruise_down_d > 0.:
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count = mcu_stepper.step_delta_const(
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mcu_time + accel_t, cruise_down_d,
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-accel_d, inv_cruise_v, -step_dist,
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height, closestxy_d, closest_height2, movez_r)
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height += count * step_dist
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if decel_down_d > 0.:
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count = mcu_stepper.step_delta_accel(
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mcu_time + decel_time_offset, decel_down_d,
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-decel_offset, -accel_multiplier, -step_dist,
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height, closestxy_d, closest_height2, movez_r)
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######################################################################
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# Matrix helper functions for 3x1 matrices
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######################################################################
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def matrix_cross(m1, m2):
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return [m1[1] * m2[2] - m1[2] * m2[1],
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m1[2] * m2[0] - m1[0] * m2[2],
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m1[0] * m2[1] - m1[1] * m2[0]]
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def matrix_dot(m1, m2):
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return m1[0] * m2[0] + m1[1] * m2[1] + m1[2] * m2[2]
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def matrix_magsq(m1):
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return m1[0]**2 + m1[1]**2 + m1[2]**2
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def matrix_sub(m1, m2):
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return [m1[0] - m2[0], m1[1] - m2[1], m1[2] - m2[2]]
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def matrix_mul(m1, s):
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return [m1[0]*s, m1[1]*s, m1[2]*s]
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