HKUST-Aerial-Robotics / Fast-Planner

A Robust and Efficient Trajectory Planner for Quadrotors
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Basis Matrix of uniform B-Spline might get wrong coefficient on arow (row 3). #93

Closed Beck-Sisyphus closed 3 years ago

Beck-Sisyphus commented 3 years ago

From the reference [17] K. Qin, "General matrix representations for b-splines", the basis matrix of uniform B-Spline with knot span of 1 looks like the following:

uniform_matrix_basis

However, at the line to Generate Uniform B-Spline, the acceleration row is << 1, -2, 1 >> instead of << 0.5, -1, 0.5 >> from the reference.

Consider to change to 1 / 2.0 for the coefficient the same as the velocity row.

Greetings, Beck

Beck-Sisyphus commented 3 years ago

My mistake. It's calculating the control point at the acceleration, and the second derivatives generates the 2x. The original coefficient are correct.