## 4 Autonomous Trajectory Planning and Optimization
### Ocean Feature Tracking  
After the rough information of the regional area is obtained, multiple vehicles are introduced to track the feature(s) of interest in the area. Figure 4 shows the frame and processes of ocean feature tracking. First, the phenomena and variations are described as a mathematical expression by which the vehicles can track and observe in feature extraction module. For example, to track temperature upwelling, the temperature is described as a scalar field with the maximum (or minimum) as the center and gradient as the variation direction and magnitude of upwelling. In order to avoid the limitations of  
Figure 4: Ocean feature tracking. observation information, multiple vehicles are proposed to move in a formation or rotational formation to obtain comprehensive information of the scalar field, and multiple sample data are employed to estimate the feature variation. The direction of movement of multiple vehicles depends on the feature extraction results and tracking missions. After the movement direction is certain, a leader-follower form is applied, that the leader vehicle tracks the movement direction, and multiple vehicles follow the leader vehicle to achieve the sample data. Those movements are defined as autonomous pursuing decision and multi vehicles cooperative control of tracking. There are certain noises in the observation data, caused by the complex background field noise and instrument noise, so KF, EKF are introduced in vehicles' cooperative control module to reduce the observation errors caused by instruments and temporal-spatial variations. Detailed descriptions are as follows:  
1. Feature extraction: Typically extracted ocean features include upwelling, fronts, gravity waves, tides, eddies. After the rough information of the ocean feature is received, an appropriate number of vehicles is selected to carry out the tracking missions. For example, when we track the two-dimensional temperature field T, the mission is described as tracking of \(\mathrm{T,VT_{x},VT_{y}}\), where \([\mathrm{VT_{x},VT_{y}}]\) is a gradient that reflects the variation of temperature. Three vehicles are enough to complete the mission if the impact of higher order derivatives of the scalar field T is neglected. Then multiple vehicles are driven to move forward intelligently along the gradient directions or in an anti-gradient direction, or an orthogonal direction to the gradient, which depends on the observation objective. 2. Autonomous pursuing decision: Autonomous pursuing decision reflects multi vehicles' cluster movement direction. The leader (or virtual leader) vehicle is defined as the multiple vehicles' formation center, and the control law of the leader's velocity and steering velocity is designed to track the feature. Then other vehicles are controlled to follow the leader in a formation. Autonomous pursuing decision combines the virtual leader vehicle tracking strategy and the actual track goals together, for example, when tracking temperature contours, first the pursuing strategy is designed to control the vehicle to move close to the contours, and then move along the temperature contours. In this process, many constraints and limitations should be taken into account, such as the actual vehicles' speed limitation, the error between the movement direction and expected direction. If the feature is lost, the predictive information can be adopted to re-position. 3. Cooperative control of tracking: After the decision of the leader moving direction is determined, the control law is applied (including velocity and location) to drive multiple vehicles following the leader, and maintain a desired formation. Multiple vehicles' formation control includes rotation, scaling and translation terms. The scaling of formation can change the size of the observation area. The qualities of observation data are different with respect to the sample location.