Bounded parameter learning
Forecast the parameter uncertainty that will remain after future observations by bounding parameter error and parameter updates, so plans can account for learning in advance.
Abstract
Robots must act safely even when their dynamics are uncertain. Robust control can protect against unknown disturbances, but it may be overly cautious when uncertainty comes from physical parameters—such as mass, friction, wind, or motor strength—that can be learned through interaction. Many adaptive controllers update their parameter estimates as data arrives, yet plan as if the initial uncertainty will persist throughout the planning horizon. This can produce unnecessarily large reachable tubes and prevent a robot from taking advantage of informative actions.
We present A-SLS, a learning-aware system-level synthesis (SLS) framework for robust adaptive control. It augments the physical state with online parameter estimates and models how those estimates evolve, preserving correlations among process disturbances, parameter errors, and estimate updates. This lets A-SLS forecast the parameter uncertainty guaranteed to remain after future observations and use that future learning when constructing reachable sets and planning safe trajectories. A GPU-compatible solver enables real-time robust adaptive model predictive control for long-horizon, high-dimensional nonlinear systems. Across robotic benchmarks, A-SLS reduces reachable-tube conservativeness while maintaining real-time performance, including whole-body control of a 61-state quadruped; a Crazyflie hardware demonstration shows online learning during flight.
Method
A-SLS makes parameter learning part of the system being controlled. After each action, it compares the observed state transition with the predicted one and uses the transition residual to update the parameter estimate and its bounded uncertainty set. The physical state and evolving estimate are then treated together as an augmented state.
For planning, A-SLS uses system-level synthesis (SLS) to build causal feedback responses that preserve the relationships between process disturbances, parameter error, and estimate updates. It forecasts how parameter uncertainty is guaranteed to shrink as future measurements arrive, then uses that reduction to construct tighter reachable tubes and plan safe trajectories. Since a trajectory affects what the robot can learn, A-SLS can also favor informative motions. Its GPU-parallel implementation scales adaptive optimization to longer planning horizons and higher-dimensional robotic systems.
Augment system + SLS
Include online parameter estimates in the system state, making estimator evolution part of the closed-loop dynamics. Then apply SLS for robust planning.
Coupled reachable tubes
Preserve correlations among disturbances, parameter errors, and estimator updates to build tighter reachable sets, instead of stacking disturbances independently.
Results
We evaluate A-SLS as a robust trajectory optimizer and as a receding-horizon controller across nonlinear robotic systems, from Dubins cars to a quadruped and a Crazyflie drone.
Dubins Car
Assured learning enables tighter tubes
On a Dubins car task with unmatched parameters, the controller plans through obstacles while accounting for dynamic uncertainty. Compared to baselines, A-SLS reduced positional tube volume to 6% and 26% of the CCM and DF baselines, respectively, while maintaining tube containment in the evaluated rollouts. The tighter tubes allow A-SLS to plan a shorter S-curve path.
Quadrotor
Actions can improve future knowledge
For a 12-state quadrotor, an information-aware objective (A-SLS+) encourages trajectories that yield higher-fidelity parameter measurements. The quadrotor moves to a higher altitude with lower disturbances; the resulting reduction in parameter uncertainty tightens its predicted position tube and improves tracking compared to A-SLS.
Quadruped
Scaling to whole-body MPC
A-SLS controls a 61-state, 12-input quadruped while learning eight joint-damping parameters in a receding-horizon model predictive control (MPC) loop. Across 40 runs, it maintained safe obstacle clearance, with a median solve time of 16.1 ms, well within the 32 ms real-time control budget.
Crazyflie; Hardware Validation
Learning on the fly
On a Crazyflie, A-SLS learns an uncertain thrust-to-acceleration parameter capturing mass, battery level, and motor health effects on the thrust command. Across 15 hardware runs, the drone recovered from a fall caused by an overly high parameter guess by using transition residuals to converge to the true parameter. This was achieved while keeping a median solve time of 8.15 ms under a 50 ms control budget.