Locomotion, Humanoids, and Navigation › Summary

Locomotion, humanoids, and navigation are the application domain where world models meet the physical body. We have seen that:

• Body dynamics and terrain interaction can involve hybrid contact modes, uncertain surfaces, and an underactuated floating base. The 1D hopper illustrates mode switching, but not every legged controller needs a latent terrain estimate or a flight mode.
• Whole-body control can connect a centroidal plan to joint torques under contact and actuator constraints. Model-based MPC predicts and replans; a direct learned policy need not follow that loop. The useful horizon and update rate are task-dependent.
• Spatial memory can support long-horizon navigation. Metric, topological, semantic, and learned maps expose different information; a map can be a probabilistic belief or a deterministic representation. Their relative value needs task-specific evaluation.
• Cross-embodiment and sim-to-real transfer require compatible interfaces and target-domain tests. Domain randomization, system identification, residual learning, and rapid adaptation address different mismatches; they do not all assume one additive dynamics residual.

The through-line is that a locomotion or navigation world model is never just $p(s_{t+1} \mid s_t, a_t)$. It is a structured composition of body, terrain, and task, each with its own uncertainty and its own failure modes, and each requiring its own evaluation. The next chapter turns to autonomous driving, where the map is a road network, the body is a car, and the road surface and other agents pose distinct prediction problems.