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Fix division with MRP #153

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merged 3 commits into from
Oct 17, 2021
Merged

Fix division with MRP #153

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4fe5482
add more inverse rotation tests
hyrodium May 2, 2021
e166a9e
fix division with MRP
hyrodium May 2, 2021
d0cfd42
fix ∇err and ∇²err
hyrodium May 2, 2021
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53 changes: 26 additions & 27 deletions src/mrps.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -56,12 +56,12 @@ function (*)(p2::MRP, p1::MRP)
end

function (\)(p1::MRP, p2::MRP)
p1,p2 = params(p1), params(p2)
n1,n2 = p1'p1, p2'p2
q1,q2 = params(p1), params(p2)
n1,n2 = q1'q1, q2'q2
θ = 1/((1+n1)*(1+n2))
s1,s2 = (1-n1), (1-n2)
v1 = -2p1
v2 = 2p2
v1 = -2q1
v2 = 2q2
s = s1*s2 - v1'v2
v = s1*v2 + s2*v1 + v1 × v2

Expand All @@ -70,18 +70,17 @@ function (\)(p1::MRP, p2::MRP)
end

function (/)(p1::MRP, p2::MRP)
n1,n2 = LinearAlgebra.norm2(p1), LinearAlgebra.norm2(p2)
q1,q2 = params(p1), params(p2)
n1,n2 = q1'q1, q2'q2
θ = 1/((1+n1)*(1+n2))
s1,s2 = (1-n1), (1-n2)
p1,p2 = params(p1), params(p2)
v1 = 2p1
v2 = -2p2
v1 = 2q1
v2 = -2q2
s = s1*s2 - v1'v2
v = s1*v2 + s2*v1 + v1 × v2

M = θ/(1+θ*s)
MRP(v[1]*M, v[2]*M, v[3]*M)

return MRP(v*M)
end


Expand Down Expand Up @@ -195,17 +194,17 @@ end
Jacobian of `p1\\p2` wrt `p2`
"""
function ∇err(p1::MRP, p2::MRP)
n1,n2 = LinearAlgebra.norm2(p1), LinearAlgebra.norm2(p2)
q1,q2 = params(p1), params(p2)
n1,n2 = q1'q1, q2'q2
θ = 1/((1+n1)*(1+n2))
s1,s2 = (1-n1), (1-n2)
p1,p2 = params(p1), params(p2)
v1 = -2p1
v2 = 2p2
v1 = -2q1
v2 = 2q2
s = s1*s2 - v1'v2
v = s1*v2 + s2*v1 + v1 × v2
dsdp = -2s1*p2 - 2v1
dvdp = 2s1*I + -2v1*p2' + 2skew(v1)
dθdp = -θ^2*(1+n1)*2p2
dsdp = -2s1*q2 - 2v1
dvdp = 2s1*I + -2v1*q2' + 2skew(v1)
dθdp = -θ^2*(1+n1)*2q2

M = θ/(1+θ*s)
dMdp = 1/(1+θ*s)*dθdp - θ/(1+θ*s)^2*(dθdp*s + θ*dsdp)
Expand All @@ -219,23 +218,23 @@ Jacobian of `(∂/∂p p1\\p2)'b` wrt `p2`
"""
function ∇²err(p1::MRP, p2::MRP, b::AbstractVector)
check_length(b, 3)
n1,n2 = LinearAlgebra.norm2(p1), LinearAlgebra.norm2(p2)
q1,q2 = params(p1), params(p2)
n1,n2 = q1'q1, q2'q2
θ = 1/((1+n1)*(1+n2))
s1,s2 = (1-n1), (1-n2)
p1,p2 = params(p1), params(p2)
v1 = -2p1
v2 = 2p2
v1 = -2q1
v2 = 2q2
s = s1*s2 - v1'v2
v = s1*v2 + s2*v1 + v1 × v2

dsdp = -2s1*p2 - 2v1 # 3x1
dsdp = -2s1*q2 - 2v1 # 3x1
dsdp2 = -2s1*I # 3x3

dvdp = 2s1*b + -2p2*v1'b - 2skew(v1)*b
dvdp = 2s1*b + -2q2*v1'b - 2skew(v1)*b
dvdp2 = -I*2v1'b

dθdp = -θ^2*(1+n1)*2p2 # 3x1
dθdp2 = -2θ*(1+n1)*2p2*dθdp' - θ^2*(1+n1)*2I # 3x3
dθdp = -θ^2*(1+n1)*2q2 # 3x1
dθdp2 = -2θ*(1+n1)*2q2*dθdp' - θ^2*(1+n1)*2I # 3x3

M = θ/(1+θ*s) # scalar
dMdp = 1/(1+θ*s)*dθdp - θ/(1+θ*s)^2*(dθdp*s + θ*dsdp) # 3x1
Expand All @@ -248,8 +247,8 @@ function ∇²err(p1::MRP, p2::MRP, b::AbstractVector)
dMdp2 -= dM3*dM2dp + dM2*dM3dp

vb = s1*v2'b + s2*v1'b + b'skew(v1)*v2 # scalar
vpdp = s1*2b' - 2p2' * (v1'b) + b'skew(v1)*2 # good
# vpdp = s1*2b' - 2p2 * (v1'b)
vpdp = s1*2b' - 2q2' * (v1'b) + b'skew(v1)*2 # good
# vpdp = s1*2b' - 2q2 * (v1'b)

d1 = M*dvdp2 + dvdp*dMdp'
d2 = dMdp2*vb + dMdp*vpdp
Expand Down
17 changes: 10 additions & 7 deletions test/rotation_tests.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -112,13 +112,16 @@ all_types = (RotMatrix{3}, AngleAxis, RotationVec,
@testset "$(R)" for R in all_types
Random.seed!(0)
for i = 1:repeats
r = rand(R)
@test inv(r) == adjoint(r)
@test inv(r) == transpose(r)
@test inv(r)*r ≈ I
@test r*inv(r) ≈ I
@test r/r ≈ I
@test r\r ≈ I
r1 = rand(R)
r2 = rand(R)
@test inv(r1) == adjoint(r1)
@test inv(r1) == transpose(r1)
@test inv(r1)*r1 ≈ I
@test r1*inv(r1) ≈ I
@test r1/r1 ≈ I
@test r1\r1 ≈ I
@test r1/r2 ≈ r1*inv(r2)
@test r1\r2 ≈ inv(r1)*r2
end
end
end
Expand Down