Reentry Trajectory Optimization Based on a Multistage Pseudospectral Method

Table 1

The key features of some well-known pseudospectral methods.

Methods	Interpolating polynomial	Type of CP*	Interval	Number of DP/CP*
CPM	𝑁 Chebyshev polynomial	Chebyshev-Gauss-Lobatto (CGL)	[−1, 1]	𝑁/𝑁
LPM	𝑁 Legendre polynomial	Legendre-Gauss-Lobatto (LGL)	[−1, 1]	𝑁/𝑁
RPM	𝑁 Legendre polynomial	Legendre-Gauss-Radau (LGR)	[−1, 1) or (−1, 1]	𝑁/𝑁−1
GPM	𝑁−1 Legendre polynomial	Legendre-Gauss (LG)	(−1, 1)	𝑁/𝑁−2

∗DP: discretization points; CP: collocation points.