Table 3 The comments of the symbols
From: Obstacle avoidance planning of space manipulator end-effector based on improved ant colony algorithm
System CM | The system’s center of gravity |
|---|---|
\(\sum {\text{I}}\) | The inertial coordinate system |
B 0 | Base of the system |
B i (i = 1,2…,7) | The ith link |
\(J_{i}\) | The ith joint |
\(C_{i}\) | Gravity center of B i |
\({\varvec{a}}_{i}\) | Position vector from J i to C i |
\({\varvec{b}}_{i}\) | The distance from C i to \(J_{i + 1}\) |
\({\varvec{b}}_{0} \in {\mathbf{R}}^{3}\) | Position vector from CM of base to joint 1 |
\({\varvec{r}}_{b} \in {\varvec{R}}^{3}\) | Position vector of the center of mass (CM) of base |
\({\varvec{r}}_{i} \in {\varvec{R}}^{3} \left( {i = 1,2, \ldots ,7} \right)\) | Position vector of CM of link \(i\) |
\({\varvec{r}}_{g} \in {\varvec{R}}^{3}\) | Position vector of the system |
\({\varvec{r}}_{e} \in {\varvec{R}}^{3}\) | Position vector of end-effector |
\({\varvec{p}}_{i} \in {\varvec{R}}^{3}\) | Position vector of joint \(i\) |
\({\varvec{p}}_{i}\) | Position vector of \(J_{i}\) |
\(\alpha_{i - 1}\) | The link corner of manipulator |
\(a_{i - 1}\) | The length of common vertical line from the joint shaft \(i - 1\) to i |
d i | The link offset |
θ i | The ith joint angle |
\({\varvec{\varTheta}} \in {\varvec{R}}^{n}\) | Joint angle vector |
m i | Mass of link i |
l i | Length of the ith link |
I | Movement inertia of the links |