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sphere_box.jl
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sphere_box.jl
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"""
SphereBoxCollision
collision between sphere and box
origin_sphere: position of sphere contact relative to body center of mass
origin_box_a: position of box corner contact a relative to body center of mass
origin_box_b: position of box corner contact b relative to body center of mass
radius_sphere: radius of sphere contact
"""
mutable struct SphereBoxCollision{T,O,I,OI} <: Collision{T,O,I,OI}
origin_sphere::SVector{I,T}
width::T
depth::T
height::T
radius_sphere::T
end
# distance
function distance(collision::SphereBoxCollision, xp, qp, xc, qc)
# contact origin points
cop = contact_point_origin(xp, qp, collision.origin_sphere)
coc = contact_point_box(cop, xc, qc, collision.width, collision.depth, collision.height)
# distance between contact origins
d = norm(cop - coc, 2)
# minimum distance between spheres
return d - collision.radius_sphere
end
function ∂distance∂x(gradient::Symbol, collision::SphereBoxCollision, xp, qp, xc, qc)
# contact origin points
cop = contact_point_origin(xp, qp, collision.origin_sphere)
coc = contact_point_box(cop, xc, qc, collision.width, collision.depth, collision.height)
# distance between contact origins
d = norm(cop - coc, 2)
∂norm∂d = ∂norm∂x(cop - coc)
if gradient == :parent
D = ∂norm∂d * (1.0 * ∂contact_point_origin∂x(xp, qp, collision.origin_sphere) - ∂contact_point_box∂p(cop, xc, qc, collision.width, collision.depth, collision.height) * ∂contact_point_origin∂x(xp, qp, collision.origin_sphere))
elseif gradient == :child
D = ∂norm∂d * -1.0 * ∂contact_point_box∂x(cop, xc, qc, collision.width, collision.depth, collision.height)
end
# if gradient == :parent
# FD = FiniteDiff.finite_difference_jacobian(x -> distance(collision, x, qp, xc, qc), xp)
# elseif gradient == :child
# FD = FiniteDiff.finite_difference_jacobian(x -> distance(collision, xp, qp, x, qc), xc)
# end
# return FD
# @assert norm(D - FD, Inf) < 1.0e-5
return D
end
function ∂distance∂q(gradient::Symbol, collision::SphereBoxCollision, xp, qp, xc, qc)
# contact origin points
cop = contact_point_origin(xp, qp, collision.origin_sphere)
coc = contact_point_box(cop, xc, qc, collision.width, collision.depth, collision.height)
# distance between contact origins
d = norm(cop - coc, 2)
∂norm∂d = ∂norm∂x(cop - coc)
if gradient == :parent
D = ∂norm∂d * (1.0 * ∂contact_point_origin∂q(xp, qp, collision.origin_sphere) - ∂contact_point_box∂p(cop, xc, qc, collision.width, collision.depth, collision.height) * ∂contact_point_origin∂q(xp, qp, collision.origin_sphere))
elseif gradient == :child
D = ∂norm∂d * -1.0 * ∂contact_point_box∂q(cop, xc, qc, collision.width, collision.depth, collision.height)
end
# if gradient == :parent
# FD = FiniteDiff.finite_difference_jacobian(q -> distance(collision, xp, Quaternion(q...), xc, qc), vector(qp))
# elseif gradient == :child
# FD = FiniteDiff.finite_difference_jacobian(q -> distance(collision, xp, qp, xc, Quaternion(q...)), vector(qc))
# end
# return FD
# @assert norm(D - FD, Inf) < 1.0e-5
return D
end
# contact point in world frame
function contact_point(relative::Symbol, collision::SphereBoxCollision, xp, qp, xc, qc)
# contact origin points
cop = contact_point_origin(xp, qp, collision.origin_sphere)
coc = contact_point_box(cop, xc, qc, collision.width, collision.depth, collision.height)
# direction of minimum distance (child to parent)
d = cop - coc
dir = normalize(d)
# contact point
if relative == :parent
return cop - collision.radius_sphere * dir
elseif relative == :child
return coc
end
end
function ∂contact_point∂x(relative::Symbol, jacobian::Symbol, collision::SphereBoxCollision, xp, qp, xc, qc)
# contact origin points
cop = contact_point_origin(xp, qp, collision.origin_sphere)
coc = contact_point_box(cop, xc, qc, collision.width, collision.depth, collision.height)
# direction of minimum distance (child to parent)
d = cop - coc
dir = normalize(d)
if relative == :parent
# cop - collision.radius_sphere * dir
if jacobian == :parent
∂c∂x = ∂contact_point_origin∂x(xp, qp, collision.origin_sphere)
X = ∂c∂x
X -= collision.radius_sphere * ∂normalize∂x(d) * (∂c∂x - ∂contact_point_box∂p(cop, xc, qc, collision.width, collision.depth, collision.height) * ∂c∂x)
elseif jacobian == :child
X = -1.0 * collision.radius_sphere * ∂normalize∂x(d) * -1.0 * ∂contact_point_box∂x(cop, xc, qc, collision.width, collision.depth, collision.height)
end
elseif relative == :child
# coc
if jacobian == :parent
X = ∂contact_point_box∂p(cop, xc, qc, collision.width, collision.depth, collision.height) * ∂contact_point_origin∂x(xp, qp, collision.origin_sphere)
elseif jacobian == :child
X = ∂contact_point_box∂x(cop, xc, qc, collision.width, collision.depth, collision.height)
end
end
# if jacobian == :parent
# FD = FiniteDiff.finite_difference_jacobian(x -> contact_point(relative, collision, x, qp, xc, qc), xp)
# elseif jacobian == :child
# FD = FiniteDiff.finite_difference_jacobian(x -> contact_point(relative, collision, xp, qp, x, qc), xc)
# end
# return FD
# @assert norm(X - FD, Inf) < 1.0e-5
return X
end
function ∂contact_point∂q(relative::Symbol, jacobian::Symbol, collision::SphereBoxCollision, xp, qp, xc, qc)
# contact origin points
cop = contact_point_origin(xp, qp, collision.origin_sphere)
coc = contact_point_box(cop, xc, qc, collision.width, collision.depth, collision.height)
# direction of minimum distance (child to parent)
d = cop - coc
dir = normalize(d)
if relative == :parent
# cop - collision.radius_sphere * dir
if jacobian == :parent
∂c∂q = ∂contact_point_origin∂q(xp, qp, collision.origin_sphere)
Q = ∂c∂q
Q -= collision.radius_sphere * ∂normalize∂x(d) * (∂c∂q - ∂contact_point_box∂p(cop, xc, qc, collision.width, collision.depth, collision.height) * ∂c∂q)
elseif jacobian == :child
Q = -1.0 * collision.radius_sphere * ∂normalize∂x(d) * -1.0 * ∂contact_point_box∂q(cop, xc, qc, collision.width, collision.depth, collision.height)
end
elseif relative == :child
# coc
if jacobian == :parent
Q = ∂contact_point_box∂p(cop, xc, qc, collision.width, collision.depth, collision.height) * ∂contact_point_origin∂q(xp, qp, collision.origin_sphere)
elseif jacobian == :child
Q = ∂contact_point_box∂q(cop, xc, qc, collision.width, collision.depth, collision.height)
end
end
# if jacobian == :parent
# FD = FiniteDiff.finite_difference_jacobian(q -> contact_point(relative, collision, xp, Quaternion(q...), xc, qc), vector(qp))
# elseif jacobian == :child
# FD = FiniteDiff.finite_difference_jacobian(q -> contact_point(relative, collision, xp, qp, xc, Quaternion(q...)), vector(qc))
# end
# return FD
# @assert norm(Q - FD, Inf) < 1.0e-5
return Q
end
function contact_normal(collision::SphereBoxCollision, xp, qp, xc, qc)
# contact points
cop = contact_point(:parent, collision, xp, qp, xc, qc)
coc = contact_point(:child, collision, xp, qp, xc, qc)
# unnormalized direction
dir = cop - coc
# distance
dis = distance(collision, xp, qp, xc, qc)
# normalized direction
if dis >= 0.0
return normalize(dir)'
else
return -1.0 * normalize(dir)'
end
end
function ∂contact_normal_transpose∂x(jacobian::Symbol, collision::SphereBoxCollision, xp, qp, xc, qc)
# contact origin points
cop = contact_point(:parent, collision, xp, qp, xc, qc)
coc = contact_point(:child, collision, xp, qp, xc, qc)
# unnormalized direction
dir = cop - coc
# Jacobians
X = ∂normalize∂x(dir) * (∂contact_point∂x(:parent, jacobian, collision, xp, qp, xc, qc) - ∂contact_point∂x(:child, jacobian, collision, xp, qp, xc, qc))
# distance
dis = distance(collision, xp, qp, xc, qc)
# normalized direction
if dis >= 0.0
return X
else
return -1.0 * X
end
end
function ∂contact_normal_transpose∂q(jacobian::Symbol, collision::SphereBoxCollision, xp, qp, xc, qc)
# contact origin points
cop = contact_point(:parent, collision, xp, qp, xc, qc)
coc = contact_point(:child, collision, xp, qp, xc, qc)
# unnormalized direction
dir = cop - coc
Q = ∂normalize∂x(dir) * (∂contact_point∂q(:parent, jacobian, collision, xp, qp, xc, qc) - ∂contact_point∂q(:child, jacobian, collision, xp, qp, xc, qc))
# Jacobians
# if jacobian == :parent
# FD = FiniteDiff.finite_difference_jacobian(q -> contact_normal(collision, xp, Quaternion(q...), xc, qc)', vector(qp))
# elseif jacobian == :child
# FD = FiniteDiff.finite_difference_jacobian(q -> contact_normal(collision, xp, qp, xc, Quaternion(q...))', vector(qc))
# end
# distance
dis = distance(collision, xp, qp, xc, qc)
# @assert norm((dis >= 0.0 ? 1.0 : -1.0) * Q - FD, Inf) < 1.0e-2
# normalized direction
if dis >= 0.0
return Q
else
return -1.0 * Q
end
end