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chengji253 / DMPC-for-multi-agent

Distributed model predictive control for multi-agent point-to-point transitions.
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关于名为Trajectory Generation for Multiagent Point-To-Point Transitions via Distributed Model Predictive Control的一些问题，想请教下您 #1

Open JingtaoQi opened 2 years ago

JingtaoQi commented 2 years ago

您好！ 我看到您复现了该论文的程序，非常感谢您的分享，我正在尝试理解论文中的理论，但是我对于文中公式（23）到公式（24）通过泰勒展开的转换难以理解，可否请教您一下？如果方便的我可以添加您的微信，或者您也可以添加我的微信13682176698.

chengji253 commented 2 years ago

那个公式我请我导师帮我推过，形式应该是没错的。主要是将近两年前的事情，具体的过程我已经忘了。你可以找数学好的老师请教一下。

JingtaoQi commented 2 years ago

我今天又推了一下，咋跟他那个不一样啊

Yeung8023 commented 1 year ago

我今天又推了一下，咋跟他那个不一样啊

I think the original equation and remarks are wrong. First, the linearization is conducted in the EQ(22), cause you can see that Vij term is a Jacobian. if you move Vij^T(Pikci_kt-1) from rho_ij to the lhs, you will get Vij^T(P(kci_kt)-Pikci_kt-1). this new term is definitely the linear increment part of EQ(22) by linearization! Second, I think the sign of epsilon in rho_ij is negative one, so you move this term to the LHS, you can get epsilon_ij^2+ Vij^T(P(kci_kt)-Pikci_kt-1). this is the whole increment of EQ(22) by Taylor expansion.