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The safety constraint for CBF handle multiple CBFs. #71

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Sep 14, 2024
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The safety constraint for CBF handle multiple CBFs. #71

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19 changes: 10 additions & 9 deletions compatible_clf_cbf/cbf.py
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Original file line number Diff line number Diff line change
Expand Up @@ -361,19 +361,19 @@ def _add_barrier_within_constraint(
"""
Adds the constraint that the 0-super level set of the barrier function
is in the safe region {x | pᵢ(x) <= 0}.
−(1+ϕ₀(x))pᵢ(x) − ϕ₁(x)h(x) is sos.
−(1+ϕ₀(x))pᵢ(x) − ∑ᵢψᵢ(x)h(x) is sos.

Note it doesn't add the constraints
ϕ₀(x) is sos
ϕ₁(x) is sos.
ϕ₀(x) is sos, ψᵢ(x) is sos.

Args:
safe_region_index: pᵢ(x) = self.safety_set.within[within_index]
"""
assert self.within_set is not None
assert lagrangians.cbf.size == 1
poly = (
-(1 + lagrangians.safe_region) * self.within_set.l[within_index]
- lagrangians.cbf * h
- lagrangians.cbf[0] * h
)
if self.state_eq_constraints is not None:
assert lagrangians.state_eq_constraints is not None
Expand All @@ -395,12 +395,12 @@ def _add_barrier_exclude_constraint(
polynomials p(x), we want to certify that the set {x|p(x)≤0, h(x)≥0}
is empty.
The emptiness of the set can be certified by the constraint
-(1+ϕ₀(x))h(x) +∑ⱼϕⱼ(x)pⱼ(x) is sos
ϕ₀(x), ϕⱼ(x) are sos.
-∑ᵢϕᵢ(x))*hᵢ(x) +∑ⱼψⱼ(x)pⱼ(x)-1 is sos
ϕᵢ(x), ψⱼ(x) are sos.

Note that this function only adds the constraint
-(1+ϕ₀(x))*hᵢ(x) +∑ⱼϕⱼ(x)pⱼ(x) is sos
It doesn't add the constraint ϕ₀(x), ϕⱼ(x) are sos.
-(1+ϕᵢ,₀(x))*hᵢ(x) +∑ⱼϕᵢ,ⱼ(x)pⱼ(x) is sos
It doesn't add the constraint ϕᵢ,₀(x), ϕᵢ,ⱼ(x) are sos.

Args:
h: a polynomial, h is the barrier function for the
Expand All @@ -409,7 +409,8 @@ def _add_barrier_exclude_constraint(
Returns:
poly: poly is the polynomial -(1+ϕ₀(x))hᵢ(x) + ∑ⱼϕⱼ(x)pⱼ(x)
"""
poly = -(1 + lagrangians.cbf) * h + lagrangians.unsafe_region.dot(
assert lagrangians.cbf.size == 1
poly = -(1 + lagrangians.cbf[0]) * h + lagrangians.unsafe_region.dot(
self.exclude_sets[exclude_set_index].l
)
if self.state_eq_constraints is not None:
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