def might_sanity_leg_lengths_check(hexapod, leg_name, points):
if not ASSERTION_ENABLED:
return
coxia = length(vector_from_to(points[0], points[1]))
femur = length(vector_from_to(points[1], points[2]))
tibia = length(vector_from_to(points[2], points[3]))
same_length = np.isclose(hexapod.coxia, coxia, atol=1)
assert same_length, wrong_length_msg(leg_name, "coxia", coxia)
same_length = np.isclose(hexapod.femur, femur, atol=1)
assert same_length, wrong_length_msg(leg_name, "femur", femur)
same_length = np.isclose(hexapod.tibia, tibia, atol=1)
assert same_length, wrong_length_msg(leg_name, "tibia", tibia)
def compute_when_triangle_can_form(self):
theta = angle_opposite_of_last_side(self.d, self.hexapod.femur,
self.hexapod.tibia)
phi = angle_between(self.coxia_to_foot_vector2d, self.leg_x_axis)
self.beta = theta - phi # case 1 or 2
if self.p3.z > 0: # case 3
self.beta = theta + phi
z_ = self.hexapod.femur * np.sin(np.radians(self.beta))
x_ = self.p1.x + self.hexapod.femur * np.cos(np.radians(self.beta))
self.p2 = Vector(x_, 0, z_)
femur_vector = vector_from_to(self.p1, self.p2)
tibia_vector = vector_from_to(self.p2, self.p3)
self.gamma = 90 - angle_between(femur_vector, tibia_vector)
if self.p2.z < self.p3.z:
raise Exception(cant_reach_alert_msg(self.leg_name, "blocking"))
def might_sanity_beta_gamma_check(beta, gamma, leg_name, points):
if not ASSERTION_ENABLED:
return
coxia = vector_from_to(points[0], points[1])
femur = vector_from_to(points[1], points[2])
tibia = vector_from_to(points[2], points[3])
result_beta = angle_between(coxia, femur)
same_beta = np.isclose(np.abs(beta), result_beta, atol=1)
assert same_beta, f"{leg_name} leg: expected: |{beta}|, found: {result_beta}"
# ❗❗IMPORTANT: Why is sometimes both are zero?
femur_tibia_angle = angle_between(femur, tibia)
is_90 = np.isclose(90, femur_tibia_angle + gamma, atol=1)
if not is_90:
alert_msg = f"{leg_name} leg:\
{femur_tibia_angle} (femur-tibia angle) + {gamma} (gamma) != 90."
print(alert_msg)
def recompute_hexapod(dimensions, ik_parameters, poses):
# make the hexapod with all angles = 0
# update the hexapod so that we know which given points are in contact with the ground
old_hexapod = VirtualHexapod(dimensions)
old_hexapod.update_stance(ik_parameters["hip_stance"],
ik_parameters["leg_stance"])
old_contacts = deepcopy(old_hexapod.ground_contacts)
# make a new hexapod with all angles = 0
# and update given the poses/ angles we've computed
new_hexapod = VirtualHexapod(dimensions)
new_hexapod.update(poses)
new_contacts = deepcopy(new_hexapod.ground_contacts)
# get two points that are on the ground before and after
# updating to the given poses
id1, id2 = find_two_same_leg_ids(old_contacts, new_contacts)
old_p1 = deepcopy(old_hexapod.legs[id1].ground_contact())
old_p2 = deepcopy(old_hexapod.legs[id2].ground_contact())
new_p1 = deepcopy(new_hexapod.legs[id1].ground_contact())
new_p2 = deepcopy(new_hexapod.legs[id2].ground_contact())
# we must translate and rotate the hexapod with the pose
# so that the hexapod is stepping on the old predefined ground contact points
old_vector = vector_from_to(old_p1, old_p2)
new_vector = vector_from_to(new_p1, new_p2)
translate_vector = vector_from_to(new_p1, old_p1)
_, twist_frame = find_twist_to_recompute_hexapod(new_vector, old_vector)
new_hexapod.rotate_and_shift(twist_frame, 0)
twisted_p2 = new_hexapod.legs[id2].foot_tip()
translate_vector = vector_from_to(twisted_p2, old_p2)
new_hexapod.move_xyz(translate_vector.x, translate_vector.y, 0)
might_sanity_check_points(new_p1, new_p2, old_p1, old_p2, new_vector,
old_vector)
return new_hexapod
def is_stable(p1, p2, p3, tol=0.001):
"""
Determines stability of the pose.
Determine if projection of 3D point p
onto the plane defined by p1, p2, p3
is within a triangle defined by p1, p2, p3.
"""
p = Vector(0, 0, 0)
u = vector_from_to(p1, p2)
v = vector_from_to(p1, p3)
n = cross(u, v)
w = vector_from_to(p1, p)
n2 = dot(n, n)
beta = dot(cross(u, w), n) / n2
gamma = dot(cross(w, v), n) / n2
alpha = 1 - gamma - beta
# then coordinate of the projected point (p_) of point p
# p_ = alpha * p1 + beta * p2 + gamma * p3
min_val = -tol
max_val = 1 + tol
cond1 = min_val <= alpha <= max_val
cond2 = min_val <= beta <= max_val
cond3 = min_val <= gamma <= max_val
return cond1 and cond2 and cond3
def store_initial_vectors(self):
self.body_to_foot_vector = vector_from_to(self.body_contact, self.foot_tip)
# find the coxia vector which is the vector
# from body contact point to joint between coxia and femur limb
projection = project_vector_onto_plane(
self.body_to_foot_vector, self.hexapod.z_axis
)
self.unit_coxia_vector = get_unit_vector(projection)
self.coxia_vector = scalar_multiply(self.unit_coxia_vector, self.hexapod.coxia)
# coxia point / joint is the point connecting the coxia and tibia limbs
coxia_point = add_vectors(self.body_contact, self.coxia_vector)
if coxia_point.z < self.foot_tip.z:
raise Exception(COXIA_ON_GROUND_ALERT_MSG)
def compute_beta_gamma_local_p2(self):
# These values are needed to compute
# p2 aka tibia joint (point between femur limb and tibia limb)
self.coxia_to_foot_vector2d = vector_from_to(self.p1, self.p3)
self.d = length(self.coxia_to_foot_vector2d)
# If we can form this triangle
# # this means we probably can reach the target ground contact point
if is_triangle(self.hexapod.tibia, self.hexapod.femur, self.d):
# CASE A: a triangle can be formed with
# coxia to foot vector, hexapod's femur and tibia
self.compute_when_triangle_can_form()
else:
# CASE B: It's impossible to reach target ground point
self.compute_when_triangle_cannot_form()
not_within_range, alert_msg = beta_gamma_not_in_range(
self.beta, self.gamma, self.leg_name)
if not_within_range:
raise Exception(alert_msg)
def inverse_kinematics_update(hexapod, ik_parameters):
tx = ik_parameters["percent_x"] * hexapod.mid
ty = ik_parameters["percent_y"] * hexapod.side
tz = ik_parameters["percent_z"] * hexapod.tibia
rotx, roty, rotz = (
ik_parameters["rot_x"],
ik_parameters["rot_y"],
ik_parameters["rot_z"],
)
hexapod.update_stance(ik_parameters["hip_stance"],
ik_parameters["leg_stance"])
hexapod.detach_body_rotate_and_translate(rotx, roty, rotz, tx, ty, tz)
if body_contact_shoved_on_ground(hexapod):
raise Exception(BODY_ON_GROUND_ALERT_MSG)
x_axis = Vector(1, 0, 0)
legs_up_in_the_air = []
for i in range(hexapod.LEG_COUNT):
leg_name = hexapod.legs[i].name
body_contact = hexapod.body.vertices[i]
foot_tip = hexapod.legs[i].foot_tip()
body_to_foot_vector = vector_from_to(body_contact, foot_tip)
# find the coxia vector which is the vector
# from body contact point to joint between coxia and femur limb
projection = project_vector_onto_plane(body_to_foot_vector,
hexapod.z_axis)
unit_coxia_vector = get_unit_vector(projection)
coxia_vector = scalar_multiply(unit_coxia_vector, hexapod.coxia)
# coxia point / joint is the point connecting the coxia and tibia limbs
coxia_point = add_vectors(body_contact, coxia_vector)
if coxia_point.z < foot_tip.z:
raise Exception(COXIA_ON_GROUND_ALERT_MSG)
# *******************
# 1. Compute p0, p1 and (possible) p3 wrt leg frame
# *******************
p0 = Vector(0, 0, 0)
p1 = Vector(hexapod.coxia, 0, 0)
# Find p3 aka foot tip (ground contact) with respect to the local leg frame
rho = angle_between(unit_coxia_vector, body_to_foot_vector)
body_to_foot_length = length(body_to_foot_vector)
p3x = body_to_foot_length * np.cos(np.radians(rho))
p3z = -body_to_foot_length * np.sin(np.radians(rho))
p3 = Vector(p3x, 0, p3z)
# *******************
# 2. Compute p2, beta, gamma and final p3 wrt leg frame
# *******************
# These values are needed to compute
# p2 aka tibia joint (point between femur limb and tibia limb)
coxia_to_foot_vector2d = vector_from_to(p1, p3)
d = length(coxia_to_foot_vector2d)
# If we can form this triangle this means
# we can probably can reach the target ground contact point
if is_triangle(hexapod.tibia, hexapod.femur, d):
# .................................
# CASE A: a triangle can be formed with
# coxia to foot vector, hexapod's femur and tibia
# .................................
theta = angle_opposite_of_last_side(d, hexapod.femur,
hexapod.tibia)
phi = angle_between(coxia_to_foot_vector2d, x_axis)
beta = theta - phi # case 1 or 2
if p3.z > 0: # case 3
beta = theta + phi
z_ = hexapod.femur * np.sin(np.radians(beta))
x_ = p1.x + hexapod.femur * np.cos(np.radians(beta))
p2 = Vector(x_, 0, z_)
femur_vector = vector_from_to(p1, p2)
tibia_vector = vector_from_to(p2, p3)
gamma = 90 - angle_between(femur_vector, tibia_vector)
if p2.z < p3.z:
raise Exception(cant_reach_alert_msg(leg_name, "blocking"))
else:
# .................................
# CASE B: It's impossible to reach target ground point
# .................................
if d + hexapod.tibia < hexapod.femur:
raise Exception(cant_reach_alert_msg(leg_name, "femur"))
if d + hexapod.femur < hexapod.tibia:
raise Exception(cant_reach_alert_msg(leg_name, "tibia"))
# Then hexapod.femur + hexapod.tibia < d:
legs_up_in_the_air.append(leg_name)
LEGS_TOO_SHORT, alert_msg = legs_too_short(legs_up_in_the_air)
if LEGS_TOO_SHORT:
raise Exception(alert_msg)
femur_tibia_direction = get_unit_vector(coxia_to_foot_vector2d)
femur_vector = scalar_multiply(femur_tibia_direction,
hexapod.femur)
p2 = add_vectors(p1, femur_vector)
tibia_vector = scalar_multiply(femur_tibia_direction,
hexapod.tibia)
p3 = add_vectors(p2, tibia_vector)
# Find beta and gamma
gamma = 0.0
leg_x_axis = Vector(1, 0, 0)
beta = angle_between(leg_x_axis, femur_vector)
if femur_vector.z < 0:
beta = -beta
# Final p1, p2, p3, beta and gamma computed at this point
not_within_range, alert_msg = beta_gamma_not_in_range(
beta, gamma, leg_name)
if not_within_range:
raise Exception(alert_msg)
# *******************
# 3. Compute alpha and twist_frame
# Find frame used to twist the leg frame wrt to hexapod's body contact point's x axis
# *******************
alpha, twist_frame = find_twist_frame(hexapod, unit_coxia_vector)
alpha = compute_twist_wrt_to_world(alpha, hexapod.body.COXIA_AXES[i])
alpha_limit, alert_msg = angle_above_limit(alpha, ALPHA_MAX_ANGLE,
leg_name, "(alpha/coxia)")
if alpha_limit:
raise Exception(alert_msg)
# *******************
# 4. Update hexapod points and finally update the pose
# *******************
points = [p0, p1, p2, p3]
might_print_points(points, leg_name)
# Convert points from local leg coordinate frame to world coordinate frame
for point in points:
point.update_point_wrt(twist_frame)
if ASSERTION_ENABLED:
assert hexapod.body_rotation_frame is not None, "No rotation frame!"
point.update_point_wrt(hexapod.body_rotation_frame)
point.move_xyz(body_contact.x, body_contact.y, body_contact.z)
might_sanity_leg_lengths_check(hexapod, leg_name, points)
might_sanity_beta_gamma_check(beta, gamma, leg_name, points)
# Update hexapod's points to what we computed
update_hexapod_points(hexapod, i, points)
poses[i]["coxia"] = alpha
poses[i]["femur"] = beta
poses[i]["tibia"] = gamma
might_print_ik(poses, ik_parameters, hexapod)
return poses, hexapod
