a
Second-order node profile. Element a(k) stores the squared path speed \((ds/dt)^2\) at station s(k).
copp.Profile3rd
Third-order path-speed profile.
Syntax
P = copp.Profile3rd(A, B)
P = ...Profile3rd(..., num_stationary=[NS0, NSF])
Description
A Profile3rd stores the two station profiles used by TOPP3/COPP3:
= \((ds/dt)^2\) \(b(k) = d^2s/dt^2\)
The stationary counters describe how many grid points at each end are treated as stationary by the third-order interpolation formulas. Solver outputs are copied into MATLAB-owned double column vectors of length N, so users do not manage native buffers or handles. A and B may be passed as row or column vectors, but obj.a and obj.b are always \(N \times 1\).
Input Arguments
b
Interval or edge acceleration profile. For TOPP2 interpolation this is an (N-1)-by-1 column vector.
Name-Value Arguments
num_stationary
Stationary interval counts [start, end] of a third-order profile. Default: [0, 0]
Properties
a
Node profile a(s) = \((ds/dt)^2\) as an \(N \times 1\) double column vector.
b
Node profile b(s) = \(d^2s/dt^2\) as an \(N \times 1\) double column vector.
num_stationary_start
Number of stationary nodes at the profile start.
num_stationary_end
Number of stationary nodes at the profile end.
len
Number of station samples in a and b.
num_stationary
Two-element vector [start, end].
Methods
Profile3rd
Construct a MATLAB-owned third-order profile.
length
Number of station samples in scalar Profile3rd objects.
force_positive_a
Adjust a and b so interpolated a(s) stays positive.
Method Details
Profile3rd
Syntax
P = copp.Profile3rd(A, B)
P = ...Profile3rd(..., num_stationary=[NS0, NSF])
copies real finite vectors A and B into \(N \times 1\) double column vectors. A and B may be \(1 \times N\) or \(N \times 1\), but they must have the same number of elements. A must be nonnegative because a(k) stores \((ds/dt)^2\).
stores the stationary-node metadata returned by TOPP3 solvers.
length
Syntax
value = length(obj)
force_positive_a
Syntax
[P, SUCCEEDED] = force_positive_a(P, S)
vector with numel(S) == P.len and at least four stations. The
Returns a copy of profile P whose a and b node values are adjusted so the third-order interpolated a(s) stays strictly positive on every interval of the station grid S. S must be a strictly increasing real finite vector with numel(S) == P.len and at least four stations. The returned object keeps the class of P, including solver-local Profile3rd aliases, and its num_stationary metadata.
SUCCEEDED is false when the adjustment failed for some interval. This is not an error, but other intervals may still have been adjusted, so keep using the original profile in that case. Invalid input raises copp:InvalidArgument: a length mismatch, fewer than four stations, negative a or a_min, non-finite values, non-increasing S, or stationary counts that leave no motion interval.
This is a numerical safety pass for profiles whose a values may touch zero because of finite precision, applied before s_to_t_topp3. It rewrites a and b without knowing the robot limits, so re-check the delivered profile with topp3">Robot.exceed_topp3 afterwards.
Name-value options: a_min: Nonnegative lower target for interpolated a. Defaults to 1e-12.
Examples
profile = copp.Profile3rd(ones(3,1), zeros(3,1), ... num_stationary=[0, 0]);