# Event-Based Path-Planning and Path-Following
## 3 Two-Level Control System
### Event-Based Path-Planning
#### 3.3.1 Discrete-Event System
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**State** & **No.** & **Composite Events** & **Next State** & **Actions** \\ \hline mS & & mPF & \(\mathcal{P}=\mathcal{P}_{\mathit{rf}}\); \(j_{r}=1\) \\ \hline mPF & 1 & (eOAN, eORVC, eOLF) or & mDOL & \(\mathcal{Q}_{L}=\) SelectObstacleLeftP(\(\mathcal{Q}\), \(j_{r}^{i}\)) \\  & 1 & (eOAN, eOLF, eORF, eWWPPBN) & mDOL & \(\mathcal{P}=\) AvoidPath(\(\mathcal{Q}_{L}\), \(\mathcal{L}\)) \\  & 2 & (eOAN, eOLVC, eORF) or & mDOR & \(\mathcal{Q}_{R}=\) SelectObstacleRightP(\(\mathcal{Q}\), \(j_{r}^{R}\)) \\  & 3 & (eOLN, eORVC) or & mDOL & \(\mathcal{Q}_{L}=\) SelectObstacleLeftP(\(\mathcal{Q}\), \(j_{r}^{L}\)) \\  & 4 & (eORN, eOLVC) or & mDOR & \(\mathcal{P}=\) AvoidPath(\(\mathcal{Q}_{L}\), \(\mathcal{L}\)) \\  & 5 & eEP & mMC & \(\mathcal{Q}_{R}=\) SelectObstacleRightP(\(\mathcal{Q}\), \(j_{r}^{R}\)) \\  & 6 & eES & mPF & \(j_{r}=j_{r}+1\) \\ \hline mNRP & 1 & mEP & mPF & \(\mathcal{P}=\mathcal{P}_{\mathit{rf}}\); IntVTState \\ \hline mDOL & 1 & (eWPB, eWPR, eWPD) or & mDOL & \(j_{r}=j_{r}+1\) \\  & 2 & eOAVC & mDOL & the same as in rule 1 of the mPF block \\  & 3 & eOLKPN & mDOL & the same as in rule 3 of the mPF block \\  & 4 & (eNORN, eOLF) & mSOR & \([\mathcal{P},j_{r}]=\) DubinsPath(\(\mathcal{P}_{\mathit{rf}},j_{r},[\mathcal{R}]\), \([\mathcal{R}]\)) \\  & 5 & or (eNOLN, eWPL, eRPPB, eWPD, eRPRL) & mNRP & \([\mathcal{P},j_{r}]=\) DubinsPath(\(\mathcal{P}_{\mathit{rf}},j_{r}\), \([\mathcal{L}]\), \([\mathcal{L}\),’\(\mathcal{R}\)’)) \\  & 6 & eEP & mDOL & \(\mathcal{Q}_{B}=\) SelectObstacleLeft(\(\mathcal{Q}\)) \\  & 2 & eOAN & mDOL & the same as in rule 1 of the mPF block \\  & 3 & eOLN & mDOL & the same as in rule 3 of the mPF block \\  & 4 & (eNOLN, eWPL, eRPSN, eRRPL) & mDOL & the same as in rule 3 of the mPF block \\  & 4 & or (eNOLN, eWPL, eRPSN, eRPRL) & mNRP & \([\mathcal{P},j_{r}]=\) DubinsPath(\(\mathcal{P}_{\mathit{rf}},j_{r}\), \([\mathcal{L}\),’\(\mathcal{L}\)’,’\(\mathcal{R}\)’)) \\  & 5 & eEP & mPF & \(\mathcal{P}=\mathcal{P}_{\mathit{rf}}\); IntVTState \\ \hline mDOR & 1 & (eWPB, eWPR, eWPD) or & mSOR & \(j_{r}=j_{r}+1\) \\  & 2 & eOAN & mDOL & the same as in rule 1 of the mPF block \\  & 3 & eOLN & mDOL & the same as in rule 3 of the mPF block \\  & 4 & (eNOLN, eORF) & mSOL & \([\mathcal{P},j_{r}]=\) DubinsPath(\(\mathcal{P}_{\mathit{rf}},j_{r}\), \([\mathcal{L}\)’), \([\mathcal{L}\)’)) \\  & 5 & or (eNORN, eWPR, eRPRP) & mNRP & \([\mathcal{P},j_{r}]=\) DubinsPath(\(\mathcal{P}_{\mathit{rf}},j_{r}\), \([\mathcal{R}\)’), \([\mathcal{L}\)’,’\(\mathcal{R}\)’)) \\  & 5 & eEP & mPR & \(\mathcal{P}=\mathcal{P}_{\mathit{rf}}\); IntVTState \\ \hline mSOL & 1 & (eWPB, eWPL, eWPD) or & mSOL & \(j_{r}=j_{r}+1\) \\  & 2 & eOAN & mDOR & the same as in rule 2 of the mPF block \\  & 3 & eORN & mDOR & the same as in rule 4 of the mPF block \\  & 4 & (eNORN, eWPR, eRPSN, eRRPR) & mSOL & \([\mathcal{P},j_{r}]=\) DubinsPath(\(\mathcal{P}_{\mathit{rf}},j_{r}\), \([\mathcal{L}\)’), \([\mathcal{L}\)’)) \\  & 5 & or (eNORN, eWPR, eRPRP, eRPRP) & mNRP & \([\mathcal{P},j_{r}]=\) DubinsPath(\(\mathcal{P}_{\mathit{rf}},j_{r}\), \([\mathcal{R}\)’), \([\mathcal{L}\)’,’\(\mathcal{R}\)’)) \\  & 6 & eEP & mDR & \(\mathcal{Q}_{B}=\) SelectObstacleRight(\(\mathcal{Q}\)) \\  & 7 & eWPDN, eRPP & mSOL & \(j_{r}=j_{r}+1\) \\  & 8 & eOAN & mDOR & the same as in rule 2 of the mPF block \\  & 9 & eONN & mDOR & the same as in rule 2 of the mPF block \\  & 10 & (eNORN, eWPR, eRPSN, eRPRP) & mNRP & \([\mathcal{P},j_{r}]=\) DubinsPath(\(\mathcal{P}_{\mathit{rf}},j_{r}\), \([\mathcal{R}\)’), \([\mathcal{L}\)’,’\(\mathcal{R}\)’)) \\  & 11 & (eWPB, eWPR, eRPRP) & mNRP & \([\mathcal{P},j_{r}]=\) DubinsPath(\(\mathcal{P}_{\mathit{rf}},j_{r}\), \([\mathcal{R}\)’), \([\mathcal{L}\)’,’\(\mathcal{R}\)’)) \\  & 12 & eEP & mPF & \(\mathcal{P}=\mathcal{P}_{\mathit{rf}}\); IntVTState \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Transition rules of the DES.