This is a study I am planning and building, to compare how much of a robot's dynamics is worth learning when the equations are already known. I am running it to extend my understanding of machine learning for robots in the real world, on top of my background in computational physics.
Premise
A torque-controlled two-link arm reaches three targets in order while avoiding an obstacle. Its rigid-body equations are known, its details are not: the arm carries an unmodelled payload, its joints stick at low speed, and its motors deliver less torque than commanded.
The controller chooses actions by simulating them with its model, so model error becomes plan error.
Given a small, fixed budget of measured transitions, there are three ways to fix the model: re-fit the physical parameters, replace the physics with a network, or keep the physics and learn only the residual. The study compares all three against the unchanged model and against the exact dynamics, inside one controller, scored by task success rather than prediction error.
- what the model predicted, 0.3 s ago
- what the arm did
- the gap, and the residual behind it
The nominal equations run forward from the state of a moment ago, under the torques actually applied (faded). The real arm, with payload, friction, and actuator error, ends up elsewhere (solid). That difference is what the residual model has to learn; the strip below traces it per joint. Computed from the study's equations, not a result.
What I expect
Structure helps early
The residual model should lead at small data budgets, since gravity, inertia, and coupling are already in the equations. The advantage should shrink as data grows.
Re-fitting has a ceiling
Fitted physics should hold up where the mismatch is parametric, such as the payload, and fall behind on sticking friction and the actuator dead zone.
Written down first
The primary contrast and the claim rule are fixed before the run. A null or opposite result is reported the same way.
An educated guess
None of the ingredients are new. Residual physics, learned models inside model-predictive control, and sampling-based planners all have prior work. What is untested is where the residual pays off and by how much, under identical data, matched capacity, one frozen controller, and claim rules fixed in advance.
The approach follows from my background. In computational physics a model that disagrees with measurement gets corrected, not discarded. A robot is the same situation: the structure is known, the deviations are small and local, and measured data is expensive.
Where it stands
Built
The simulator, verified against analytic, energy, and reference integrator checks. Target worlds, five model conditions, matched training, the planner, evaluation, and bootstrap analysis, run end to end on a smoke configuration.
Open
Task calibration. Under the draft task parameters even the exact-dynamics reference fails, so the task is being fixed before any model is trained on it.
Results
None yet. This page will be expanded as the study runs.