bv_cvxbook_extra_exercises

Some nodes are xed and their coordinate vectors xj

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: = 4, S = 0.8, V to = 40, L = 300. Plot pt , vt , ft , and bt versus t. Comment on what you see. Report the take-oﬀ time and take-oﬀ position for the proﬁle you ﬁnd. 14.8 Optimal spacecraft landing. We consider the problem of optimizing the thrust proﬁle for a spacecraft to carry out a landing at a target position. The spacecraft dynamics are mp = f − mge3 , ¨ where m > 0 is the spacecraft mass, p(t) ∈ R3 is the spacecraft position, with 0 the target landing position and p3 (t) representing height, f (t) ∈ R3 is the thrust force, and g > 0 is the gravitational acceleration. (For simplicity we assume that the spacecraft mass is constant. This is not always a good assumption, since the mass decreases with fuel use. We will also ignore any atmospheric friction.) We must have p(T td ) = 0 and p(T td ) = 0, where T td is the touchdown time. The ˙ spacecraft must remain in a region given by p3 (t) ≥ α (p1 (t), p2 (t)) 2 , where α > 0 is a given minimum glide slope. The initial position p(0) and velocity p(0) are given. ˙ The thrust force...
View Full Document

Ask a homework question - tutors are online