kinematics: Add deltesian printers (#5743)

Initial push of the working deltesian kinematics after some successful tests.

Signed-off-by: Fabrice GALLET <tircown@gmail.com>

1 files changed, 184 insertions, 0 deletions

diff --git a/klippy/kinematics/deltesian.py b/klippy/kinematics/deltesian.py
new file mode 100644
index 00000000..bb231370
--- /dev/null
+++ b/klippy/kinematics/deltesian.py
@@ -0,0 +1,184 @@
+# Code for handling the kinematics of deltesian robots
+#
+# Copyright (C) 2022  Fabrice Gallet <tircown@gmail.com>
+#
+# This file may be distributed under the terms of the GNU GPLv3 license.
+import math, logging
+import stepper
+
+# Slow moves once the ratio of tower to XY movement exceeds SLOW_RATIO
+SLOW_RATIO = 3.
+
+# Minimum angle with the horizontal for the arm to not exceed - in degrees
+MIN_ANGLE = 5.
+
+class DeltesianKinematics:
+    def __init__(self, toolhead, config):
+        self.rails = [None] * 3
+        stepper_configs = [config.getsection('stepper_' + s)
+                                    for s in ['left', 'right', 'y']]
+        self.rails[0] = stepper.PrinterRail(
+            stepper_configs[0], need_position_minmax = False)
+        def_pos_es = self.rails[0].get_homing_info().position_endstop
+        self.rails[1] = stepper.PrinterRail(
+            stepper_configs[1], need_position_minmax = False,
+            default_position_endstop = def_pos_es)
+        self.rails[2] = stepper.LookupMultiRail(stepper_configs[2])
+        arm_x = self.arm_x = [None] * 2
+        arm_x[0] = stepper_configs[0].getfloat('arm_x_length', above=0.)
+        arm_x[1] = stepper_configs[1].getfloat('arm_x_length', arm_x[0],
+                                                above=0.)
+        arm = [None] * 2
+        arm[0] = stepper_configs[0].getfloat('arm_length', above=arm_x[0])
+        arm[1] = stepper_configs[1].getfloat('arm_length', arm[0],
+                                              above=arm_x[1])
+        arm2 = self.arm2 = [a**2 for a in arm]
+        self.rails[0].setup_itersolve(
+            'deltesian_stepper_alloc', arm2[0], -arm_x[0])
+        self.rails[1].setup_itersolve(
+            'deltesian_stepper_alloc', arm2[1], arm_x[1])
+        self.rails[2].setup_itersolve('cartesian_stepper_alloc', b'y')
+        for s in self.get_steppers():
+            s.set_trapq(toolhead.get_trapq())
+            toolhead.register_step_generator(s.generate_steps)
+        config.get_printer().register_event_handler(
+            "stepper_enable:motor_off", self._motor_off)
+        self.limits = [(1.0, -1.0)] * 3
+        # X axis limits
+        min_angle = config.getfloat('min_angle', MIN_ANGLE,
+                                    minval=0., maxval=90.)
+        cos_angle = math.cos(math.radians(min_angle))
+        x_kin_min = math.ceil( -min(arm_x[0], cos_angle * arm[1] - arm_x[1]))
+        x_kin_max = math.floor( min(arm_x[1], cos_angle * arm[0] - arm_x[0]))
+        x_kin_range = min(x_kin_max - x_kin_min, x_kin_max * 2, -x_kin_min * 2)
+        print_width = config.getfloat('print_width', None, minval=0.,
+                                      maxval=x_kin_range)
+        if print_width:
+            self.limits[0] = (-print_width * 0.5, print_width * 0.5)
+        else:
+            self.limits[0] = (x_kin_min, x_kin_max)
+        # Y axis limits
+        self.limits[1] = self.rails[2].get_range()
+        # Z axis limits
+        pmax = [r.get_homing_info().position_endstop for r in self.rails[:2]]
+        self._abs_endstop = [p + math.sqrt(a2 - ax**2) for p, a2, ax
+                    in zip( pmax, arm2, arm_x )]
+        self.home_z = self._actuator_to_cartesian(self._abs_endstop)[1]
+        z_max = min([self._pillars_z_max(x) for x in self.limits[0]])
+        z_min = config.getfloat('minimum_z_position', 0, maxval=z_max)
+        self.limits[2] = (z_min, z_max)
+        # Limit the speed/accel if is is at the extreme values of the x axis
+        slow_ratio = config.getfloat('slow_ratio', SLOW_RATIO, minval=0.)
+        self.slow_x2 = self.very_slow_x2 = None
+        if slow_ratio > 0.:
+            sr2 = slow_ratio ** 2
+            self.slow_x2 = min([math.sqrt((sr2 * a2) / (sr2 + 1))
+                        - axl for a2, axl in zip(arm2, arm_x)]) ** 2
+            self.very_slow_x2 = min([math.sqrt((2 * sr2 * a2) / (2 * sr2 + 1))
+                        - axl for a2, axl in zip(arm2, arm_x)]) ** 2
+            logging.info("Deltesian kinematics: moves slowed past %.2fmm"
+                         " and %.2fmm"
+                         % (math.sqrt(self.slow_x2),
+                            math.sqrt(self.very_slow_x2)))
+        # Setup boundary checks
+        max_velocity, max_accel = toolhead.get_max_velocity()
+        self.max_z_velocity = config.getfloat('max_z_velocity', max_velocity,
+                                              above=0., maxval=max_velocity)
+        self.max_z_accel = config.getfloat('max_z_accel', max_accel,
+                                           above=0., maxval=max_accel)
+        self.axes_min = toolhead.Coord(*[l[0] for l in self.limits], e=0.)
+        self.axes_max = toolhead.Coord(*[l[1] for l in self.limits], e=0.)
+        self.homed_axis = [False] * 3
+        self.set_position([0., 0., 0.], ())
+    def get_steppers(self):
+        return [s for rail in self.rails for s in rail.get_steppers()]
+    def _actuator_to_cartesian(self, sp):
+        arm_x, arm2 = self.arm_x, self.arm2
+        dx, dz = sum(arm_x), sp[1] - sp[0]
+        pivots = math.sqrt(dx**2 + dz**2)
+        # Trilateration w/ reference frame along left to right pivots
+        xt = (pivots**2 + arm2[0] - arm2[1]) / (2 * pivots)
+        zt = math.sqrt(arm2[0] - xt**2)
+        # Rotation and translation of the reference frame
+        x = xt * dx / pivots + zt * dz / pivots - arm_x[0]
+        z = xt * dz / pivots - zt * dx / pivots + sp[0]
+        return [x, z]
+    def _pillars_z_max(self, x):
+        arm_x, arm2 = self.arm_x, self.arm2
+        dz = (math.sqrt(arm2[0] - (arm_x[0] + x)**2),
+              math.sqrt(arm2[1] - (arm_x[1] - x)**2))
+        return min([o - z for o, z in zip(self._abs_endstop, dz)])
+    def calc_position(self, stepper_positions):
+        sp = [stepper_positions[rail.get_name()] for rail in self.rails]
+        x, z = self._actuator_to_cartesian(sp[:2])
+        return [x, sp[2], z]
+    def set_position(self, newpos, homing_axes):
+        for rail in self.rails:
+            rail.set_position(newpos)
+        for n in homing_axes:
+            self.homed_axis[n] = True
+    def home(self, homing_state):
+        homing_axes = homing_state.get_axes()
+        home_xz = 0 in homing_axes or 2 in homing_axes
+        home_y = 1 in homing_axes
+        forceaxes = ([0, 1, 2] if (home_xz and home_y) else
+                     [0, 2] if home_xz else [1] if home_y else [])
+        homing_state.set_axes(forceaxes)
+        homepos = [None] * 4
+        if home_xz:
+            homing_state.set_axes([0, 1, 2] if home_y else [0, 2])
+            homepos[0], homepos[2] = 0., self.home_z
+            forcepos = list(homepos)
+            dz2 = [(a2 - ax ** 2) for a2, ax in zip(self.arm2, self.arm_x)]
+            forcepos[2] = -1.5 * math.sqrt(max(dz2))
+            homing_state.home_rails(self.rails[:2], forcepos, homepos)
+        if home_y:
+            position_min, position_max = self.rails[2].get_range()
+            hi = self.rails[2].get_homing_info()
+            homepos[1] = hi.position_endstop
+            forcepos = list(homepos)
+            if hi.positive_dir:
+                forcepos[1] -= 1.5 * (hi.position_endstop - position_min)
+            else:
+                forcepos[1] += 1.5 * (position_max - hi.position_endstop)
+            homing_state.home_rails([self.rails[2]], forcepos, homepos)
+    def _motor_off(self, print_time):
+        self.homed_axis = [False] * 3
+    def check_move(self, move):
+        limits = list(map(list, self.limits))
+        spos, epos = move.start_pos, move.end_pos
+        homing_move = False
+        if epos[0] == 0. and epos[2] == self.home_z and not move.axes_d[1]:
+            # Identify a homing move
+            homing_move = True
+        elif epos[2] > limits[2][1]:
+            # Moves at the very top - adapt limits depending on the X position
+            limits[2][1] = self._pillars_z_max(epos[0])
+        for i in (i for i, v in enumerate(move.axes_d[:3]) if v):
+            if not self.homed_axis[i]:
+                raise move.move_error("Must home axis first")
+            # Move out of range - verify not a homing move
+            if epos[i] < limits[i][0] or epos[i] > limits[i][1]:
+                if not homing_move:
+                    raise move.move_error()
+        if move.axes_d[2]:
+            z_ratio = move.move_d / abs(move.axes_d[2])
+            move.limit_speed(
+                self.max_z_velocity * z_ratio, self.max_z_accel * z_ratio)
+        # Limit the speed/accel if is is at the extreme values of the x axis
+        if move.axes_d[0] and self.slow_x2 and self.very_slow_x2:
+            move_x2 = max(spos[0] ** 2, epos[0] ** 2)
+            if move_x2 > self.very_slow_x2:
+                move.limit_speed(self.max_velocity *0.25, self.max_accel *0.25)
+            elif move_x2 > self.slow_x2:
+                move.limit_speed(self.max_velocity *0.50, self.max_accel *0.50)
+    def get_status(self, eventtime):
+        axes = [a for a, b in zip("xyz", self.homed_axis) if b]
+        return {
+            'homed_axes': "".join(axes),
+            'axis_minimum': self.axes_min,
+            'axis_maximum': self.axes_max,
+        }
+
+def load_kinematics(toolhead, config):
+    return DeltesianKinematics(toolhead, config)