Update README.md

README.md

@@ -24,8 +24,15 @@ pipeline_tag: video-text-to-text
 
 An end-to-end Vision-Language-Action (VLA) trajectory planning model for autonomous driving based on **Qwen-Drive-4B**, fine-tuned with **LoRA** and a **Differentiable Kinematic Unicycle Planner** on the **nuScenes** dataset.
 ![Simulation](simulation.gif)
-Instead of standard independent coordinate regression (which often causes spatial teleportation and dynamically infeasible maneuvers), this model predicts physically constrained longitudinal accelerations $a_t$ and yaw rates $\omega_t$ over a **5.0-second horizon** ($50 \text{ steps} \times 0.1\text{s} \; dt$). Coordinates $(x, y, \psi)$ are integrated via a differentiable kinematic model (`torch.cumsum`).
+Instead of standard independent coordinate regression (which often causes spatial teleportation and dynamically infeasible maneuvers), this model predicts physically constrained longitudinal accelerations $a_t$ and yaw rates $\omega_t$ over a 5.0-second horizon ($50\text{ steps}$ at $\Delta t = 0.1\text{ s}$).
 
+Future vehicle coordinates $(x, y, \psi)$ are dynamically integrated via a differentiable kinematic motion model:
+
+$$v_t = \max\left(0, \, v_0 + \sum_{\tau=1}^t a_\tau \Delta t\right)$$
+
+$$\psi_t = \sum_{\tau=1}^t \omega_\tau \Delta t$$
+
+$$x_t = \sum_{\tau=1}^t v_\tau \cos(\psi_\tau) \Delta t, \quad y_t = \sum_{\tau=1}^t v_\tau \sin(\psi_\tau) \Delta t$$
 ---
 
 ## 🏆 Key Benchmarks & Results (nuScenes Validation)