Dual Control

Safe navigation in interactive traffic requires autonomous vehicles to reason about unobservable human characteristics and the reciprocal nature of multi-agent interactions. Traditional architectures often decouple prediction from planning, leading to the "Frozen Robot Problem" or unsafe maneuvers under high ambiguity because they treat risk assessment and information acquisition as independent objectives. We argue that the notion of safety should not remain static but must instead dynamically co-evolve with the system's internal confidence: the robot should actively clarify ambiguity when necessary while also recognizing the diminishing returns of information, and naturally transition toward task execution. We introduce a unified belief-space Model Predictive Control (MPC) framework that couples multistep information planning with a clarity-adaptive Conditional Value-at-Risk (CVaR) barrier mechanism. By treating clarity, a scalar informational state, as an explicit planning variable, the controller co-designs its probing strategy with its safety specification, tightening conservatism under high ambiguity and relaxing constraints as confidence improves. We further provide a performance analysis showing that the cost of information seeking and the expected planning-cost gap to a controller that knows the true human characteristic are bounded by residual ambiguity and solver error. We evaluate the framework in lane-merging and unsignalized-intersection scenarios against representative interactive-planning baselines. Across 5,000 simulations, the proposed method achieves the highest success rates (94.6% and 93.2%) and the lowest collision rates (1.2% and 1.4%) among the compared methods, providing a principled foundation for robust decision-making in human-centric environments.

In dynamical systems, feedback can improve performance by allowing decisions to depend on past observations, rather than being designed a priori. Under full observation, the current state is sufficient for decision-making; under partial observation, the controller must instead estimate the state from measurements. When actions also affect observations, control can have a dual role: actions influence both the state and the information available for future decisions. This interaction can invalidate certainty-equivalent (CE) control, a widely used strategy that applies state feedback policies as if the estimated state were the true state. We ask when this suboptimality leads to a quantitative performance gap that grows with the horizon. We study this question in a linear-quadratic system with bilinear observations by comparing the optimal policy, certainty-equivalent control, and the optimal open-loop (OL) policy. We identify an instance-dependent information-strength parameter $q$ and establish distinct performance regimes as $q$ varies. When $q$ is sufficiently small, we show that no policy can improve over OL control by more than $O(1)$ cumulative cost. For large values of $q$, we find that CE achieves an $Ω(T)$ advantage over OL control. Our main finding is that for intermediate values of $q$, we can construct a policy that occasionally probes for information and achieves an $Ω(T)$ advantage over OL control while CE only achieves an $O(1)$ advantage, establishing an $Ω(T)$ gap between CE and optimal control. Our analysis relies on a regret decomposition that captures the tradeoff between the immediate cost of gathering information and its future benefit.

Robust adaptive control is vital for keeping robots safe while actively reducing uncertainty in unfamiliar settings. However, traditional methods are often conservative since they fail to account for guaranteed future parameter learning during planning and struggle to scale to high-dimensional systems. In this work, we present A-SLS, a learning-aware robust adaptive model predictive control (RAMPC) framework based on system-level synthesis. A-SLS forecasts future parameter uncertainty and preserves correlations between process disturbances, parameter error, and estimate updates to construct tight, guaranteed reachable sets that account for future information gain. We also develop a GPU-accelerated A-SLS solver to enable real-time performance. Across nonlinear robotic systems, A-SLS reduces reachable-tube conservativeness, maintains real-time performance, and scales to whole-body control for a quadruped with 61 states, 8 uncertain parameters, and 12 control inputs. We further demonstrate the approach on hardware, where a physical Crazyflie drone learns an uncertain dynamics parameter online to stabilize on the fly.

Controlling a hybrid system to a target set under parameter uncertainty can require informative actions that temporarily drive the system state away from the specified set. We propose a belief-informed dual-control algorithm that combines belief-space receding-horizon selection with an expected-decrease constraint on a nonnegative target-set progress function. To accommodate exploratory deviations, a scalar controller state bounds the constraint's cumulative slack. Our algorithm's two-step lookahead selection uses predicted observations to update the parameter belief before evaluating the subsequent action's admissibility. Under distance-comparison bounds, correct conditional prediction, and recursive feasibility, we prove almost-sure target-set convergence at decision times and bound both the sum of expected progress-function values and the expected neighborhood-entry time. Upper confidence bounds extend these convergence guarantees to bounded model samples with summable error probabilities. In planar regulation with an unknown control direction, we verify recursive feasibility: the proposed two-step selection reduces the Euclidean state norm below 0.01 within 11 decisions for either sign, whereas a myopic one-step selection loses admissibility immediately after zero input. In a simulated bimanual assembly task, our algorithm's one-step implementation uses clearance feedback to complete the assembly under nominal friction, yielding a 96.4% lower infinity-norm relative-position error than the reference-tracking baseline at the method's completion time. At lower friction, its posterior conditioning successfully detects an empty admissible set, whereas a fixed-prior alternative admits an action that violates the conditional decrease constraint. Project page: https://clintonenwerem.com/belief-hybrid-control/.

This paper develops a fast numerical dual control for exploration and exploitation (DCEE) method to address auto-optimization problems in unknown environments. In auto-optimization problems, the optimal operating condition is unknown a priori and may vary with the environment. As in classical dual control techniques, computational burden remains a major concern in DCEE for active learning. Existing DCEE methods provide a principled exploration-exploitation objective, but mainly realized through standard optimization packages or explicit gradient-type update laws, where the numerical structure of the DCEE has not been fully exploited. This paper shows that the reward function in DCEE has an inherent convex-over-nonlinear structure, where the exploitation and exploration terms form a unified nonlinear residual map equipped with a convex outer loss. Benefiting from this structure, a structure-exploiting numerical method is developed by linearizing only the nonlinear residual map while preserving the convex outer loss. Thus, each subproblem is transformed into a structured convex form that can be solved reliably. The resulting generalized Gauss-Newton Hessian approximation is positive semidefinite and depends only on first-order derivatives, thereby supporting fast online computation. The proposed method is evaluated on a vehicle cruising auto-optimization problem and compared with existing methods. Simulation and hardware-in-the-loop experimental results show that the proposed method improves control performance and achieves a speedup of approximately one order of magnitude, with a microsecond-level maximum computation time of only 83 μs on a typical vehicle embedded CPU.

We study finite-horizon quadratic control of linear systems with bilinear observations, in which the control input affects not only the state dynamics but also the partial observations of the state. In this setting, the separation principle can fail because control inputs influence the future quality of state estimates. State estimation requires an input-dependent Kalman filter whose gain and error covariance evolve as functions of the control inputs. To address this challenge, we propose a belief-space model predictive control ($\texttt{B-MPC}$) method that plans directly over both the estimated state and its error covariance. In particular, $\texttt{B-MPC}$ plans with a deterministic surrogate of the belief evolution defined by the input-dependent Kalman filter. Through numerical experiments in two synthetic settings, we show that $\texttt{B-MPC}$ can outperform both the separation-principle controller and its MPC variant in favorable regimes, and that these gains are accompanied by lower estimation covariance and more uncertainty-aware action choices.

Planning safe trajectories under model uncertainty is a fundamental challenge. Robust planning ensures safety by considering worst-case realizations, yet ignores uncertainty reduction and leads to overly conservative behavior. Actively reducing uncertainty on-the-fly during a nominal mission defines the dual control problem. Most approaches address this by adding a weighted exploration term to the cost, tuned to trade off the nominal objective and uncertainty reduction, but without formal consideration of when exploration is beneficial. Moreover, safety is enforced in some methods but not in others. We study a budget-constrained dual control problem, where uncertainty is reduced subject to safety and a mission-level cost budget that limits the allowable degradation in task performance due to exploration. In this work, we propose Dual-gatekeeper, a framework that integrates robust planning with active exploration under formal guarantees of safety and budget feasibility. The key idea is that exploration is pursued only when it provides a verifiable improvement without compromising safety or violating the budget, enabling the system to balance immediate task performance with long-term uncertainty reduction in a principled manner. We provide two implementations of the framework based on different safety mechanisms and demonstrate its performance on quadrotor navigation and autonomous car racing case studies under parametric uncertainty.

Model-based control can achieve reliable task performance, but its effectiveness depends on the accuracy of the underlying model. Robots operating under model uncertainty must often adapt to previously unseen payloads, objects, and interaction dynamics to complete a task successfully. Conventional approaches typically rely on a dedicated task- and control-agnostic excitation phase for estimating physics parameters, delaying task execution and collecting potentially irrelevant data. In this paper, we instead consider zero-shot task execution under parametric uncertainty, where online model learning and control proceed concurrently during task execution. Our approach formulates reference generation within a dual control framework to produce task-relevant, informative trajectories that reduce parameter uncertainty in directions critical to task success. We predefine a feedback policy with an explicit parameter adaptation law and optimize the reference through the resulting adaptive closed-loop dynamics. We propose two formulations: 1) minimizing expected task cost under parameter uncertainty, and 2) minimizing optimality loss, which quantifies the degradation in task performance caused by planning with an incorrect parameter estimate. By actively optimizing for informative trajectories via a natural Fisher information measure, we tightly approach a lower bound on task-relevant parameter uncertainty while simultaneously achieving reliable task execution. Across diverse tasks, controllers, and adaptation laws, targeted exploration enables the identification required for successful task execution, allowing robots to learn relevant physical parameters while completing the task in a single attempt.