Testing Synchronization Simulation Speed with Unreal Visualization

Problem

• MuJoCo simulation (mj_step()) does not guarantee real-time execution.
• Unreal Engine renders frames at real-time pace (e.g., 60fps).
• Without adjustment, the visualized motion in Unreal won't match real-world timing.
• If MuJoCo is faster or slower, we must scale Unreal’s time to match it.

---

Key Concepts

Concept	Description
timestep (mjModel.opt.timestep)	Simulation step size in seconds (e.g., 0.002 = 500Hz).
simulated_time	MuJoCo internal clock (mjData.time).
real_time_passed	Real-world clock elapsed time.
simulation_speed	Ratio of MuJoCo simulated time to real-world time. simulation_speed = simulated_time / real_time_passed

Goal: Keep simulation_speed ≈ 1.0 for realistic visualization.

---

Setup Instructions

1. Set a Good MuJoCo Timestep

• Choose mjModel.opt.timestep based on your robot’s control loop frequency.
• Recommended: 0.001 (1kHz) or 0.002 (500Hz).

Example:

model.opt.timestep = 0.002;  // 500Hz

---

2. Measure Simulation Speed

Track two times:

• MuJoCo Time: mjData.time
• Real Clock Time: Use high-res system timer (e.g., std::chrono::steady_clock).

Calculate each frame:

simulation_speed = (mjData.time - mjDataStart) / (realTimeNow - realTimeStart)

Interpretation:

• simulation_speed > 1.0 → MuJoCo is faster than real-time → Speed up Unreal.
• simulation_speed < 1.0 → MuJoCo is slower than real-time → Slow down Unreal.

---

3. Adjust Unreal Engine Time

Use Unreal’s Global Time Dilation to sync:

UGameplayStatics::SetGlobalTimeDilation(GetWorld(), simulation_speed);

MuJoCo Speed	Unreal Time Dilation
2.0x faster	2.0
0.5x slower	0.5

---

4. Handle Skip Frames / Multiple Steps

• Unreal runs at ~60fps.
• MuJoCo might need multiple steps per Unreal frame.
• Example: if MuJoCo timestep = 0.002s (500Hz), and Unreal is 60fps:
  • 0.002s * 8 steps = 0.016s → matches ~60Hz frame time.

Typical Unreal frame update:

for (int i = 0; i < numMuJoCoStepsPerFrame; ++i)
    mj_step(model, data);

---

Full Quick Checklist

| Parameter