Locomotion, Humanoids, and Navigation › Limitations and Impact

The modeling and planning methods in this chapter are useful in legged and mobile robotics, but they carry limitations that affect system design and evaluation.

The first limitation is that contact-mode changes are difficult for a single smooth predictor to represent accurately. A model fitted across a switch can blur the event or mistime it, as the hopper experiment showed. Contact schedules, event predictors, and discrete mode variables make the switch explicit; contact-implicit optimization instead keeps the contact decision inside a constrained numerical problem. Each choice trades modeling detail against computational and estimation demands.

The second limitation is that one-step prediction quality need not imply good decisions. Error can accumulate under rollout and can be concentrated near task-critical contact events. A limited bound shows what can be concluded. For one fixed open-loop action sequence $a_{0:H-1}$, suppose each stage cost and the terminal cost are $L$-Lipschitz in state, the same actions are evaluated by both models, and both trajectories start from the same state. Then:

$$\left| C_{\text{model}}(a_{0:H-1}) - C_{\text{true}}(a_{0:H-1}) \right| \leq L \sum_{t=0}^{H} \| \hat{s}_t - s_t \|$$

Here $\hat{s}_t$ and $s_t$ are the modeled and true states reached under that same action sequence. The bound follows by applying the Lipschitz condition to each cost term and then the triangle inequality. It does not compare two different policies. To bound the regret from choosing actions with the model, one additionally needs a uniform bound $\left|C_{\text{model}}(a)-C_{\text{true}}(a)\right|\leq\delta$ for every candidate sequence in a common feasible set. If $a_{\text{model}}$ minimizes modeled cost and $a_{\text{true}}$ minimizes true cost over that set, then $0\leq C_{\text{true}}(a_{\text{model}})-C_{\text{true}}(a_{\text{true}})\leq 2\delta$. A small error on one observed trajectory alone does not supply that uniform guarantee.

The evaluation question "does this world model help you act?" is the one that matters for locomotion, and it is not answered by looking at one-step prediction loss. We return to this in depth in Part XI, Ch 4: Planning, Control, and Policy Evaluation.

The third limitation is model exploitation in optimization. An MPC optimizer can prefer a plan that relies on contact forces the physical robot cannot generate if its model or constraints permit them. Friction, actuator, and balance constraints can rule out some such plans when their parameters and contact assumptions are valid, but the constraints can also be wrong. Structured prior knowledge helps narrow the search; it does not by itself establish hardware safety. Identification, monitoring, and closed-loop tests remain necessary.

The fourth limitation is sim-to-real mismatch. A new body, payload, sensor, or terrain can change which simulator errors matter. Domain randomization, system identification, and residual learning have reduced specific gaps in published systems, but their effects are not automatic or interchangeable. Deployment-specific characterization and fallback behavior may be useful; this chapter does not establish how frequently companies use a particular fallback design.

The fifth limitation is data coverage. Physical-robot trajectories can be costly and valuable for validating real contact and sensing, while simulation can provide more controlled variation at lower collection cost. Required data volume and the best data source depend on the model and task. Pretrained approaches discussed in Part IX: Foundation and World-Action Models may reduce per-deployment data in some settings, but cross-embodiment locomotion transfer still needs measured evidence.

The sixth limitation is that navigation can require distinct estimates of metric layout, semantic content, and moving agents. A system may represent them separately or jointly. If dynamic obstacles or doors are not updated, a route planned from an older map can become invalid. Testing map updates and distinguishing persistent from changing structure matter when people or other agents share the space.

These methods are relevant to deployed robots, but deployment evidence should be named and measured rather than inferred from the toy experiments. Boston Dynamics documents Spot use on construction sites, and warehouse operators document mobile-robot fleets. This chapter does not quantify fleet-wide daily floor area, establish a single dominant humanoid deployment pattern, or attribute every deployment's success to one world-model family. Explicit mapping, model-based control, and learned dynamics are different design choices whose contribution must be evaluated in each system.