# Trajectory Planning with Time-Variant Safety Margin for Autonomous Vehicle Lane Change +
## 3 Experimental Verification
### Simulation with Random Traffic  
In order to achieve a dynamic traffic environment for the experiment, a microscopic road traffic simulation is designed. Here Intelligent Driver Model in [22] is employed to generate the traffic flow with vehicle cruise control. The proposed lane change maneuver algorithm is evaluated in a four-lane highway test scene. At the start of simulation, traffic vehicles are created within certain range from an arbitrary point on the road. Each vehicle is given a random initial speed and target speed by using normal distribution \(N\left(\mu_{v},\sigma_{v}{}^{2}\right)\), and an upper and lower limitation is set to avoid the unrealistic speeds. For The distances between traffic vehicles are initialized with logarithmic normal distribution \(N\left(\mu_{t},\sigma_{t}{}^{2}\right)\). The fitting functions and their parameters \(\mu_{v}\), \(\sigma_{v}\), \(\mu_{t}\) and \(\sigma_{t}\) are determined using real road traffic records in [23]. Based on the Intelligent Driver Model, the desired acceleration of traffic vehicles is calculated by their current speed and target speed. The initialized vehicle which has closest longitudinal distance to the origin is selected as the host vehicle \(V_{H}\). The lane change simulation is evaluated on the 100 versions of the traffic scenarios. Each traffic scenario is simulated with one minute. The random vehicle states in each traffic scenario are generated with the same set of seeds, so the simulation scenarios for different methods can be consistent with each other. There are two kinds of continuous trajectory planning methods. One is time-based re-planning method (TBRP) which take re-planning algorithm with a constant time interval. A balance should be found between the algorithm complexity and efficiency. Another one is condition-based re-planning  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Symbol** & **Value** & **Symbol** & **Value** & **Symbol** & **Value** \\ \hline \(t_{1}\) & 0.5 s & \(t_{2}\) & 1.0 s & \(a_{dyn}\) & 9 m/s\({}^{2}\) \\ \(q_{1x}\) & 1 & \(q_{2x}\) & 10 & \(q_{3x}\) & 1 \\ \(q_{1y}\) & 1 & \(q_{2y}\) & 10 & \(q_{3y}\) & 1 \\ \(t_{g}\)  
To verify the effect of the proposed condition-based re-planning (CBRP) algorithm, a time-based re-planning (TBRP) method is compared in the simulation. TBRP represents conventional methods for path planning, which take re-planning algorithm with a constant time interval. This method has good effectiveness and robustness, but the computation complexity is a challenge for the real-time implementation. The CBRP method takes re-planning algorithm by a predefined trigger mechanism. This method has less amount of calculation than TBRP, but the final performance needs a good design of control logic. In order to show the improvement, the comparative indices of the lane change control is defined as: Numbers of LC, Numbers of RP (re-planning), Average LC Time, Average Acceleration, Average Speed and Total Computing Time. Here the computing time is achieved by the simulation time in MATLAB environment. The results of one hundred random traffic scenarios are presented in Table 3. Since the simulated traffic flow is designed with varying vehicle speed, the target speed of each vehicle is randomly selected within an interval of 15\(\sim\)30 \(\mathrm{m/s}\), and updates independently per a random time interval between 5 and 20 s. The host vehicle will control to take lane change maneuver, and its target speed is set to 25 \(\mathrm{m/s}\). The performance of lane change maneuver is compared between TBRP and CBRP. To show the influence of the time-variant safety margin, results of CBRP with a conservative (CBRP-C) and aggressive (CBRP-A) settings are investigated. For CBRP-C, the gain coefficients of safety margin are set as \(K_{F}=K_{R}=1.0\), while for CBRP-A, are set as \(K_{F}=K_{R}=0.5\). Compared to the results of TBRP, the lane change control of CBRP has lower numbers of RP, and smaller average acceleration.