- #1
jumbo1985
- 19
- 1
Suppose I have a arbitrary path X(u) for u∈[0,1] of length L.
I want to traverse the path at a variable speed (I'm only really concerned about the magnitude of velocity). I want the graph of my speed function σ(t) to have the shape of a sigmoid and I want it to start at an arbitrary value s0 and be bounded by an arbitrary value s1. There's a bound on the maximum magnitude of acceleration equal to A. I want to get to my maximum speed or s1 as fast as possible while not going over the acceleration limit.
From basic calculus and physics I know that:
[tex] L = \int_{0}^{t}\sigma(t) dt[/tex]
I know the value of L. I know that my function will be some form of
[tex]\sigma_{1}(t) = 1/(1+e^{-t})[/tex]
There's a lot that I don't know unfortunately.
Is there a way to build my function σ(t) other than guessing? If not, how to best go about making intelligent guesses so that I eventually converge to my desired function?
Any suggestions welcome. Thanks!
I want to traverse the path at a variable speed (I'm only really concerned about the magnitude of velocity). I want the graph of my speed function σ(t) to have the shape of a sigmoid and I want it to start at an arbitrary value s0 and be bounded by an arbitrary value s1. There's a bound on the maximum magnitude of acceleration equal to A. I want to get to my maximum speed or s1 as fast as possible while not going over the acceleration limit.
From basic calculus and physics I know that:
[tex] L = \int_{0}^{t}\sigma(t) dt[/tex]
I know the value of L. I know that my function will be some form of
[tex]\sigma_{1}(t) = 1/(1+e^{-t})[/tex]
There's a lot that I don't know unfortunately.
Is there a way to build my function σ(t) other than guessing? If not, how to best go about making intelligent guesses so that I eventually converge to my desired function?
Any suggestions welcome. Thanks!
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