A pivotal brain computation relies on the ability to sustain perception-action loops. Stochastic optimal control theory offers a mathematical framework to explain these processes at the algorithmic level through optimality principles. However, incorporating a realistic noise model of the sensorimotor system -- accounting for multiplicative noise in feedback and motor output, as well as internal noise in estimation -- makes the problem challenging. Currently, the algorithm that is commonly used is the one proposed in the seminal study in (Todorov, 2005). After discovering some pitfalls in the original derivation, i.e., unbiased estimation does not hold, we improve the algorithm by proposing an efficient gradient descent-based optimization that minimizes the cost-to-go while only imposing linearity of the control law. The optimal solution is obtained by iteratively propagating in closed form the sufficient statistics to compute the expected cost and then minimizing this cost with respect to the filter and control gains. We demonstrate that this approach results in a significantly lower overall cost than current state-of-the-art solutions, particularly in the presence of internal noise, though the improvement is present in other circumstances as well, with theoretical explanations for this enhanced performance. Providing the optimal control law is key for inverse control inference, especially in explaining behavioral data under rationality assumptions.

This paper presents a real-time control framework for nonlinear pure-feedback systems with unknown dynamics to satisfy reach-avoid-stay tasks within a prescribed time in dynamic environments. To achieve this, we introduce a real-time spatiotemporal tube (STT) framework. An STT is defined as a time-varying ball in the state space whose center and radius adapt online using only real-time sensory input. A closed-form, approximation-free control law is then derived to constrain the system output within the STT, ensuring safety and task satisfaction. We provide formal guarantees for obstacle avoidance and on-time task completion. The effectiveness and scalability of the framework are demonstrated through simulations and hardware experiments on a mobile robot and an aerial vehicle, navigating in cluttered dynamic environments.

Mecanum wheeled mobile robots (MWMRs) are highly susceptible to actuator faults that degrade performance and risk mission failure. Current fault tolerant control (FTC) schemes for MWMRs target complete actuator failures like motor stall, ignoring partial faults e.g., in torque degradation. We propose an FTC strategy handling both fault types, where we adopt posterior probability to learn real-time fault parameters. We derive the FTC law by aggregating probability-weighed control laws corresponding to predefined faults. This ensures the robustness and safety of MWMR control despite varying levels of fault occurrence. Simulation results demonstrate the effectiveness of our FTC under diverse scenarios.

This paper presents a Spatiotemporal Tube (STT)-based control framework for differential-drive mobile robots with dynamic uncertainties and external disturbances, guaranteeing the satisfaction of Temporal Reach-Avoid-Stay (T-RAS) specifications. The approach employs circular STT, characterized by smoothly time-varying center and radius, to define dynamic safe corridors that guide the robot from the start region to the goal while avoiding obstacles. In particular, we first develop a sampling-based synthesis algorithm to construct a feasible STT that satisfies the prescribed timing and safety constraints with formal guarantees. To ensure that the robot remains confined within this tube, we then design analytically a closed-form, approximation-free control law. The resulting controller is computationally efficient, robust to disturbances and {model uncertainties}, and requires no model approximations or online optimization. The proposed framework is validated through simulation studies on a differential-drive robot and benchmarked against state-of-the-art methods, demonstrating superior robustness, accuracy, and computational efficiency.

Vector fields are advantageous in handling nonholonomic motion planning as they provide reference orientation for robots. However, additionally incorporating curvature constraints becomes challenging, due to the interconnection between the design of the curvature-bounded vector field and the tracking controller under underactuation. In this paper, we present a novel framework to co-develop the vector field and the control laws, guiding the nonholonomic robot to the target configuration with curvature-bounded trajectory. First, we formulate the problem by introducing the target positive limit set, which allows the robot to converge to or pass through the target configuration, depending on different dynamics and tasks. Next, we construct a curvature-constrained vector field (CVF) via blending and distributing basic flow fields in workspace and propose the saturated control laws with a dynamic gain, under which the tracking error's magnitude decreases even when saturation occurs. Under the control laws, kinematically constrained nonholonomic robots are guaranteed to track the reference CVF and converge to the target positive limit set with bounded trajectory curvature. Numerical simulations show that the proposed CVF method outperforms other vector-field-based algorithms. Experiments on Ackermann UGVs and semi-physical fixed-wing UAVs demonstrate that the method can be effectively implemented in real-world scenarios.

We present a Riccati-based framework for safety-critical nonlinear control that integrates the barrier states (BaS) methodology with the State-Dependent Riccati Equation (SDRE) approach. The BaS formulation embeds safety constraints into the system dynamics via auxiliary states, enabling safety to be treated as a control objective. To overcome the limited region of attraction in linear BaS controllers, we extend the framework to nonlinear systems using SDRE synthesis applied to the barrier-augmented dynamics and derive a matrix inequality condition that certifies forward invariance of a large region of attraction and guarantees asymptotic safe stabilization. The resulting controller is computed online via pointwise Riccati solutions. We validate the method on an unstable constrained system and cluttered quadrotor navigation tasks, demonstrating improved constraint handling, scalability, and robustness near safety boundaries. This framework offers a principled and computationally tractable solution for synthesizing nonlinear safe feedback in safety-critical environments.

Over the past few decades, continuous quaternion-based attitude control has been proven highly effective for driving rotational systems that can be modeled as rigid bodies, such as satellites and drones. However, methods rooted in this approach do not enforce the existence of a unique closed-loop (CL) equilibrium attitude-error quaternion (AEQ); and, for rotational errors about the attitude-error Euler axis larger than πrad, their proportional-control effect diminishes as the system state moves away from the stable equilibrium of the CL rotational dynamics. In this paper, we introduce a new type of attitude control law that more effectively leverages the attitude-error Euler axis-angle information to guarantee a unique CL equilibrium AEQ and to provide greater flexibility in the use of proportional-control efforts. Furthermore, using two different control laws as examples-through the construction of a strict Lyapunov function for the CL dynamics-we demonstrate that the resulting unique equilibrium of the CL rotational system can be enforced to be uniformly asymptotically stable. To assess and demonstrate the functionality and performance of the proposed approach, we performed numerical simulations and executed dozens of real-time tumble-recovery maneuvers using a small quadrotor. These simulations and flight tests compellingly demonstrate that the proposed axis-angle-based method achieves superior flight performance-compared with that obtained using a high-performance quaternion-based controller-in terms of stabilization time.

This paper presents a decentralized control framework that incorporates social awareness into multi-agent systems with unknown dynamics to achieve prescribed-time reach-avoid-stay tasks in dynamic environments. Each agent is assigned a social awareness index that quantifies its level of cooperation or self-interest, allowing heterogeneous social behaviors within the system. Building on the spatiotemporal tube (STT) framework, we propose a real-time STT framework that synthesizes tubes online for each agent while capturing its social interactions with others. A closed-form, approximation-free control law is derived to ensure that each agent remains within its evolving STT, thereby avoiding dynamic obstacles while also preventing inter-agent collisions in a socially aware manner, and reaching the target within a prescribed time. The proposed approach provides formal guarantees on safety and timing, and is computationally lightweight, model-free, and robust to unknown disturbances. The effectiveness and scalability of the framework are validated through simulation and hardware experiments on a 2D omnidirectional

This letter presents a systematic framework for switching between different sets of outputs for the control of nonlinear systems via feedback linearization. We introduce the concept of a meld to formally define a valid, feedback-linearizable subset of outputs that can be selected from a larger deck of possible outputs. The main contribution is a formal proof establishing that under suitable dwell-time and compatibility conditions, it is possible to switch between different melds while guaranteeing the uniform boundedness of the system state. We further show that the error dynamics of the active outputs remain exponentially stable within each switching interval and that outputs common to consecutive melds are tracked seamlessly through transitions. The proposed theory is valid for any feedback linearizable nonlinear system, such as, e.g., robots, aerial and terrestrial vehicles, etc.. We demonstrate it on a simple numerical simulation of a robotic manipulator.

This work addresses the problem of designing a visual servo controller for a multirotor vehicle, with the end goal of tracking a moving spherical target with unknown radius. To address this problem, we first transform two bearing measurements provided by a camera sensor into a bearing-angle pair. We then use this information to derive the system's dynamics in a new set of coordinates, where the angle measurement is used to quantify a relative distance to the target. Building on this system representation, we design an adaptive nonlinear control algorithm that takes advantage of the properties of the new system geometry and assumes that the target follows a constant acceleration model. Simulation results illustrate the performance of the proposed control algorithm.