# Reducing Safety Risks in Construction Tower Crane Operations: A Dynamic Path Planning Model
## 2 A Dynamic Path Planning Model for Tower Crane Operations
### Path Planning Module
The trajectory evaluation function of the TC-DWA algorithm consists of three sub-functions:  
\[G(v,\omega)=\sigma[\alpha\times heading(v,\omega)+\beta\times dist(v,\omega)+\gamma \times vel(v,\omega)] \tag{3}\]  
where \(\alpha,\beta,\gamma\) are the weights corresponding to each sub-function; \(heading(v,\omega)\) indicates the deviation between the endpoint of the simulated trajectory and the target point, with smaller values signifying closer trajectories; \(dist(v,\omega)\) represents the distance between the simulated trajectory and protected objects, with larger values indicating safer trajectories; \(vel(v,\omega)\) signifies the current motion speed, where higher values allow for quicker approaches to the endpoint. A higher value of the total trajectory evaluation function \(G(v,\omega)\) signifies better overall trajectory performance. To balance the impact of various indicators on the evaluation results, normalization is applied to the three sub-evaluation functions, as shown in Equation (3) [49]. The motion modes of the tower crane are categorized into boom rotation and trolley amplitude adjustment. Each mode requires a corresponding kinematic model. The kinematic equation for the boom rotation model is shown in Equation (4). \[\left\{ \begin{array}{l}x=r\times\cos(yaw+d\theta)\\ y=r\times\sin(yaw+d\theta)\\ d\theta=w\times dt\end{array} \right. \tag{4}\]  
The kinematic equation for the trolley amplitude adjustment is shown in Equation (5). \[\left\{ \begin{array}{l}x=x+v\times\cos(yaw)\times dt\\ y=y+v\times\sin(yaw)\times dt\end{array} \right. \tag{5}\]  
where \(yaw\) is the current yaw angle, and \(d\theta\) is equal to the angular velocity \(w\) multiplied by the time increment \(dt\). The framework of the path optimization algorithm is illustrated in Figure 6. It outlines the steps involved in the TC-DWA algorithm for optimizing the tower crane's operational path. The process begins with the collection of real-time data from the crane's environment, followed by the identification of obstacles and the potential drop zones. Next, the algorithm evaluates the current trajectory based on various constraints, including speed, acceleration, and safety distances from protected objects. The trajectory evaluation function incorporates multiple criteria to ensure a smooth and safe path, adjusting as necessary based on dynamic environmental feedback. Finally, the algorithm generates an optimized path that balances efficiency and safety, allowing the tower crane to perform its tasks effectively while minimizing risks to workers and equipment. Figure 6: Framework of path optimization algorithm for tower crane operations. This model aims to optimize the dynamic path of tower cranes during operation, ensuring the safe transportation of lifted loads while minimizing the risk of drops affecting ground workers, and striving to select the shortest path. In certain situations, when the current motion state is unable to execute the planned route, a switch in motion mode will be implemented. In the long-distance operation scenario, the tower crane is responsible for transporting loads from the material storage area to the worker's operation area on the main construction site. During this phase, the transportation range is extensive, and the rotation angle is significant, which may necessitate traversing around critical equipment. A common scenario is illustrated in Figure 7.  
The path optimization strategy is as follows:  
* Initially assess the distance L1 from the tower crane to the material storage area and the distance L2 to the worker's operation area. * If L1 > L2, initialize the motion mode to linear movement of the trolley to reduce the rotation radius, adjusting the crane's rotation radius L1 to L2. * Throughout the operation, if the forward path encounters critical equipment, switch the motion mode to minimize the radius for obstacle avoidance. Upon successful avoidance, revert to the rotation mode.