Robust Control

Transferring heavy payloads in maritime settings relies on efficient crane operation, limited by hazardous double-pendulum payload sway. This sway motion is further exacerbated in offshore environments by external perturbations from wind and ocean waves. Manual suppression of these oscillations on an underactuated crane system by human operators is challenging. Existing control methods struggle in such settings, often relying on simplified analytical models, while deep reinforcement learning (RL) approaches tend to generalise poorly to unseen conditions. Deploying a predictive controller onto compute-constrained, highly non-linear physical systems without relying on extensive offline training or complex analytical models remains a significant challenge. Here we show a complete real-time control pipeline centered on the MuJoCo MPC framework that leverages a cross-entropy method planner to evaluate candidate action sequences directly within a physics simulator. By using simulated rollouts, this sampling-based approach successfully reconciles the conflicting objectives of dynamic target tracking and sway damping without relying on complex analytical models. We demonstrate that the controller can run effectively on a resource-constrained embedded hardware, while outperforming traditional PID and RL baselines in counteracting external base perturbations. Furthermore, our system demonstrates robustness even when subjected to unmodeled physical discrepancies like the introduction of a second payload.

Underactuated robots are characterized by a larger number of degrees of freedom than actuators and if they are designed with a specific mass distribution, they can be controlled by means of differential flatness theory. This structural property enables the development of lightweight and cost-effective robotic systems with enhanced dexterity. However, a key challenge lies in managing the passive joints, whose control demands precise and comprehensive dynamic modeling of the system. To simplify dynamic models, particularly for low-speed trajectories, friction is often neglected. While this assumption simplifies analysis and control design, it introduces residual oscillations of the end-effector about the target position. In this paper, the possibility of using optimal control along with differential flatness control is investigated to improve the tracking of the planned trajectories. First, the study was carried out through formal analysis, and then, it was validated by means of numerical simulations. Results highlight that optimal control can be used to plan the flat variables considering different (quadratic) performance indices: control effort, i.e. motor torque, and potential energy of the considered underactuated joint. Moreover, the minimization of potential energy can be used to design motion laws that are robust against variation of the stiffness and damping of the underactuated joint, thus reducing oscillations in the case of stiffness/damping mismatch.

Co-design optimisation of autonomous systems has emerged as a powerful alternative to sequential approaches by jointly optimising physical design and control strategies. However, existing frameworks often neglect the robustness required for autonomous systems navigating unstructured, real-world environments. For agile Unmanned Aerial Vehicles (UAVs) operating at the edge of the flight envelope, this lack of robustness yields designs that are sensitive to perturbations and model mismatch. To address this, we propose a robust co-design framework for agile fixed-wing UAVs that integrates parametric uncertainty and wind disturbances directly into the concurrent optimisation process. Our bi-level approach optimises physical design in a high-level loop while discovering nominal solutions via a constrained trajectory planner and evaluating performance across a stochastic Monte Carlo ensemble using feedback LQR control. Validated across three agile flight missions, our strategy consistently outperforms deterministic baselines. The results demonstrate that our robust co-design strategy inherently tailors aerodynamic features, such as wing placement and aspect ratio, to achieve an optimal trade-off between mission performance and disturbance rejection.

Animal brains exhibit remarkable efficiency in perception and action, while being robust to both external and internal perturbations. The means by which brains accomplish this remains, for now, poorly understood, hindering our understanding of animal and human cognition, as well as our own implementation of efficient algorithms for control of dynamical systems.A potential candidate for a robust mechanism of state estimation and action computation is the free energy principle, but existing implementations of this principle have largely relied on conventional, biologically implausible approaches without spikes. We propose a novel, efficient, and robust spiking control framework with realistic biological characteristics. The resulting networks function as free energy constrainers, in which neurons only fire if they reduce the free energy of their internal representation. The networks offer efficient operation through highly sparse activity while matching performance with other similar spiking frameworks, and have high resilience against both external (e.g. sensory noise or collisions) and internal perturbations (e.g. synaptic noise and delays or neuron silencing) that such a network would be faced with when deployed by either an organism or an engineer. Overall, our work provides a novel mathematical account for spiking control through constraining free energy, providing both better insight into how brain networks might leverage their spiking substrate and a new route for implementing efficient control algorithms in neuromorphic hardware.

The stability and control of Unmanned Aerial Vehicles (UAVs) in a turbulent environment is a matter of great concern. Devising a robust control algorithm to reject disturbances is challenging due to the highly nonlinear nature of wind dynamics, and modeling the dynamics using analytical techniques is not straightforward. While traditional techniques using disturbance observers and classical adaptive control have shown some progress, they are mostly limited to relatively non-complex environments. On the other hand, learning based approaches are increasingly being used for modeling of residual forces and disturbance rejection; however, their generalization and interpretability is a factor of concern. To this end, we propose a novel integration of data-driven system identification using Sparse Identification of Non-Linear Dynamics (SINDy) with a Recursive Least Square (RLS) adaptive control to adapt and reject wind disturbances in a turbulent environment. We tested and validated our approach on Gazebo harmonic environment and on real flights with wind speeds of up to 2 m/s from four directions, creating a highly dynamic and turbulent environment. Adaptive SINDy outperformed the baseline PID and INDI controllers on several trajectory tracking error metrics without crashing. A root mean square error (RMSE) of up to 12.2 cm and 17.6 cm, and a mean absolute error (MAE) of 13.7 cm and 10.5 cm were achieved on circular and lemniscate trajectories, respectively. The validation was performed on a very lightweight Crazyflie drone under a highly dynamic environment for complex trajectory tracking.

This paper presents a systematic framework for computing formally guaranteed trajectory tracking error bounds for autonomous helicopters based on Robust Positive Invariant (RPI) sets. The approach establishes a closed-loop translational error dynamics which is cast into polytopic linear parameter-varying form with bounded additive and state-dependent disturbances. Ellipsoidal RPI sets are computed, yielding explicit position error bounds suitable as certified buffer zones in upper-level trajectory planning. Three controller architectures are compared with respect to the conservatism of their error bounds and tracking performance. Simulation results on a nonlinear helicopter model demonstrate that all architectures satisfy the derived bounds, while highlighting trade-offs between performance and the conservatism of the computed invariant set.

Aerial manipulation (AM) expands UAV capabilities beyond passive observation to contact-based operations at high altitudes and in otherwise inaccessible environments. Although recent advances show promise, most AM systems are developed in controlled settings that overlook key aerodynamic effects. Simplified thrust models are often insufficient to capture the nonlinear wind disturbances and proximity-induced flow variations present in real-world environments near infrastructure, while high-fidelity CFD methods remain impractical for real-time use. Learning-based models are computationally efficient at inference, but often struggle to generalize to unseen condition. This paper combines both approaches by integrating a physics-based blade-element model with a learning-based residual force estimator, along with a rotor-speed allocation strategy for disturbance compensation, resulting in a unified control framework. The blade-element model computes per-rotor aerodynamic forces under wind and provides a refined feedforward disturbance estimate. A learning-based estimator then predicts the residual forces not captured by the model, enabling compensation for unmodeled aerodynamic effects. An online adaptation mechanism further updates the residual-force prediction and rotor-speed allocation jointly to reduce the mismatch between desired and realized thrust. We evaluate this framework in both free-flight and wall-contact tracking tasks in a simulated near-wall wind environment. Results demonstrate improved disturbance estimation and trajectory-tracking accuracy over conventional approaches, enabling robust wall-contact execution under challenging aerodynamic conditions.

Robotic systems deployed beyond controlled environments encounter abrupt and unobserved dynamics shifts that induce substantial transient performance loss, even when the nominal closed loop remains locally stabilizing. We formulate rapid inference-time recovery for physical AI as a constrained residual learning problem, in which an online correction added to a frozen reinforcement learning policy is regulated to minimize recovery time while remaining inside the robustness margin of the nominal controller. We specifically focus upon the regulation of residual's corrective authority relative to an already competent frozen policy. The learned residual produces bounded action-space corrections online, and a Stability Alignment Gate regulates this corrective authority through magnitude constraints, directional coherence, performance-conditioned regulation, and adaptive gain modulation. The method requires no environment resets, policy retraining, explicit system identification, or privileged shift information. Across mid-episode changes in actuation, mass, and contact conditions, it reduces recovery time relative to frozen SAC by up to 87% on Go1, 48% on Cassie, 30% on H1, and 20% on Scout in simulation, while preserving near-nominal steady-state performance. The framework is also characterized on two physical robots, a Trossen ViperX manipulator and an AgileX Scout Mini, cutting recovery time by 19.5% on hardware without modifying onboard controller or accessing shift information.

A key challenge towards reliable robotic control is devising computational models that can both learn policies and guarantee robustness when deployed in the field. Inspired by the free energy principle in computational neuroscience, to address these challenges, we propose a model for policy computation that jointly learns environment dynamics and rewards, while ensuring robustness to epistemic uncertainties. Expounding a distributionally robust free energy principle, we propose a modification to the maximum diffusion learning framework. After explicitly characterizing robustness of our policies to epistemic uncertainties in both environment and reward, we validate their effectiveness on continuous-control benchmarks, via both simulations and real-world experiments involving manipulation with a Franka Research~3 arm. Across simulation and zero-shot deployment, our approach narrows the sim-to-real gap, and enables repeatable tabletop manipulation without task-specific fine-tuning.

Contact-rich micromanipulation in microfluidic flow is challenging because small disturbances can break pushing contact and induce large lateral drift. We study planar cell pushing with a magnetic rolling microrobot that tracks a waypoint-sampled reference curve under time-varying Poiseuille flow in simulation. We propose a hybrid controller that augments a nominal MPC with a learned residual policy trained by SAC. The policy outputs a bounded 2D velocity correction that is contact-gated, so residual actions are applied only during robot-cell contact, preserving reliable approach behavior and stabilizing learning. All methods share the same actuation interface and speed envelope for fair comparisons. Simulation results show improved robustness and tracking accuracy over pure MPC and PID under nonstationary flow, with generalization from a clover training curve to unseen circle and square trajectories. A residual-bound sweep identifies an intermediate correction limit as the best trade-off, which we use in all benchmarks.

Analyzing nonlinear systems with attracting robust invariant sets (RISs) requires estimating their domains of attraction (DOAs). Despite extensive research, accurately characterizing DOAs for general nonlinear systems remains challenging due to both theoretical and computational limitations, particularly in the presence of uncertainties and state constraints. In this paper, we propose a novel framework for the accurate estimation of safe (state-constrained) and robust DOAs for discrete-time nonlinear uncertain systems with continuous dynamics, open safe sets, compact disturbance sets, and uniformly locally $\ell_p$-stable compact RISs. The notion of uniform $\ell_p$ stability is quite general and encompasses, as special cases, uniform exponential and polynomial stability. The DOAs are characterized via newly introduced value functions defined on metric spaces of compact sets. We establish their fundamental mathematical properties and derive the associated Bellman-type (Zubov-type) functional equations. Building on this characterization, we develop a physics-informed neural network (NN) framework to learn the corresponding value functions by embedding the derived Bellman-type equations directly into the training process. To obtain certifiable estimates of the safe robust DOAs from the learned neural approximations, we further introduce a verification procedure that leverages existing formal verification tools. The effectiveness and applicability of the proposed methodology are demonstrated through four numerical examples involving nonlinear uncertain systems subject to state constraints, and its performance is compared with existing methods from the literature.

We present a runtime efficient algorithm for autonomous helicopter landings on moving ship decks based on Shrinking-Horizon Model Predictive Control (SHMPC). First, a suitable planning model capturing the relevant aspects of the full nonlinear helicopter dynamics is derived. Next, we use the SHMPC together with a touchdown controller stage to ensure a pre-specified maneuver time and an associated landing time window despite the presence of disturbances. A high disturbance rejection performance is achieved by designing an ancillary controller with disturbance feedback. Thus, given a target position and time, a safe landing with suitable terminal conditions is be guaranteed if the initial optimization problem is feasible. The efficacy of our approach is shown in simulation where all maneuvers achieve a high landing precision in strong winds while satisfying timing and operational constraints with maximum computation times in the millisecond range.

Solving safety-critical control problem has widely adopted the Control Barrier Function (CBF) method. However, the existence of a CBF is only a sufficient condition for system safety. The recently proposed Taylor-Lagrange Control (TLC) method addresses this limitation, but is vulnerable to the feasibility preservation problem (e.g., inter-sampling effect). In this paper, we propose a robust TLC (rTLC) method to address the feasibility preservation problem. Specifically, the rTLC method expands the safety function at an order higher than the relative degree of the function using Taylor's expansion with Lagrange remainder, which allows the control to explicitly show up at the current time instead of the future time in the TLC method. The rTLC method naturally addresses the feasibility preservation problem with only one hyper-parameter (the discretization time interval size during implementation), which is much less than its counterparts. Finally, we illustrate the effectiveness of the proposed rTLC method through an adaptive cruise control problem, and compare it with existing safety-critical control methods.

Robust control of mechanical systems with multiple uncertainties remains a fundamental challenge, particularly when nonlinear dynamics and operating-condition variations are intricately intertwined. Although deep reinforcement learning combined with domain randomization has shown promise in mitigating the sim-to-real gap, simultaneously handling all the sources of uncertainty often leads to sub-optimal policies and poor learning efficiency. This study proposes continual uncertainty learning (CUL), a curriculum-based continual learning framework for robust control of nonlinear systems on which multiple heterogeneous uncertainties are simultaneously superimposed. The core idea is to decompose the original control problem into a sequence of continual learning tasks by extending the system into a set of plants whose uncertainties are progressively expanded and diversified, so that the strategy for handling each uncertainty is acquired sequentially. Within this curriculum, the policy is updated across the plant sets under a memory-efficient anti-forgetting regularization, which preserves the strategies acquired for earlier uncertainties. In parallel, a model-based controller that guarantees a shared baseline performance across all the plant sets is embedded in the learning process, so that the agent learns only the residual compensation for each uncertainty, thereby substantially enhancing sample efficiency. The proposed framework is applied to the design of an active vibration controller for automotive powertrains as a practical industrial application. Comparative validation demonstrates that the resulting controller remains robust against structural nonlinearities and dynamic variations over a wide range of plant conditions while improving the control performance.

In this paper, a Lyapunov-based synthesis of a PI-like controller is proposed for robust trajectory tracking of an independently driven and steered four-wheel mobile robot. For the robot considered in this work, an explicit structurally verified mathematical model is used to enable systematic controller design with rigorous stability guarantees suitable for real time implementation. An augmented Lyapunov-based practical stability analysis is developed for the combined velocity-error and integral-error dynamics of the inner loop, yielding explicit bounds and sufficient conditions for practical stability and uniform ultimate boundedness of the combined velocity-error and integral-error state. The resulting control law retains a PI-like structure with model-based feedforward compensation, making it suitable for implementation on standard embedded platforms while improving robustness against configuration dependent residual dynamics and unmodelled effects. The effectiveness and robustness of the proposed design are demonstrated experimentally on a four-wheel independently steered and independently driven mobile robot platform, under both horizontal and vertical operating conditions and benchmarked against a PI controller and a sliding-mode controller.

Robotic cutting is a challenging, contact-rich manipulation task where the robot must simultaneously negotiate unknown object mechanics, large contact forces, and precise motion requirements. Our hypothesis is that this complexity can be alleviated through the design of a physically structured virtual-model controller that uses switched virtual mechanisms to generate a robust, rhythmic rock-chop motion for robotic cutting, without requiring pre-planned trajectories or precise environmental information. Motion is generated by the interaction between the environment, the robot's dynamics, and the virtual forces of the switching virtual mechanism, ultimately realized through the available actuation. Through theoretical and numerical analysis, together with experimental validation, we demonstrate that the controlled robot behavior settles into a stable periodic motion. Experiments with a Franka manipulator demonstrate robust cuts across five different vegetables, achieving sub-millimeter slice accuracy for thicknesses from 1 mm to 7 mm at a rate of nearly one cut per second. The controller maintains high performance despite changes in knife shape or cutting board height, and successfully adapts to a different humanoid manipulator, demonstrating robustness and platform independence.

Uncertainties and disturbances in robotic systems, such as aerodynamic forces, are fundamentally outcomes of physical interactions with the environment, manifesting as learnable spatiotemporal sequences rather than random noise. However, achieving high-precision control for robotic systems operating in unstructured environments is often hindered by complex unmodeled dynamics and external disturbances. While learning-based methods offer powerful approximation capabilities, they typically suffer from heavy reliance on offline training and lack theoretical guarantees. Conversely, traditional robust control strategies are predominantly reactive, limited to instantaneous estimation without the foresight to anticipate future disturbance trends. To bridge this gap, this paper proposes a differentiable data-enabled Koopman control framework termed DEKC. Unlike black-box approaches, DEKC adopts a hybrid modeling strategy that retains the nominal physics model while employing a deep neural network to parameterize the lifting function of Koopman operator for unknown residual dynamics. Crucially, the framework formulates disturbances as a dynamical system, learning their temporal evolution in a global linear space. This enables the prediction of future disturbance trajectories, which are explicitly integrated into controller for preemptive compensation. Furthermore, an online backward gradient update mechanism is introduced to ensure real-time adaptation to time-varying uncertainties. Numerical simulations on a tethered space robot demonstrate the efficacy of the proposed DEKC in mitigating highly coupled uncertainties. Complementing these results, real-world experiments on a quadrotor substantiate its superiority in tracking agile trajectories under uncertainties induced by aerodynamics and suspended payload.

This paper presents an immersive bilateral teleoperation framework for beyond-human-scale manipulators, combining motion/force transparency with enhanced operator embodiment through virtual reality (VR) and distributed haptic feedback. The platform integrates a full-scale industrial hydraulic manipulator, a 7-DoF haptic exoskeleton, and head-tracked visual feedback to reinforce operator agency and self-location. A force-sensorless adaptive controller incorporates an augmented human-robot dynamic model to address master-surrogate asymmetries, input nonlinearities, model uncertainties, and communication delays. Rigorous analysis establishes semi-global uniform ultimate boundedness of the closed-loop system. Extensive full-scale experiments demonstrate precise motion and force tracking with scaling up to 1:13 and 1:1000, respectively, and fixed or time-varying delays up to 150 ms. Coordinated 6-DoF pick-and-place and multi-axis contact tasks further validate system performance. A ten-participant user study supports system usability and indicates approximately 50% higher normalized embodiment scores with VR than with monitor-based feedback. These results advance intuitive, force-reflected remote manipulation at industrial scale.

A robust control strategy for autonomous vehicles can improve system stability, enhance riding comfort, and prevent driving accidents. This paper presents a novel interpolation-tubebased constrained iterative linear quadratic regulator (itubeCILQR) algorithm for autonomous computer-vision-based vehicle lane-keeping. The goal of the algorithm is to enhance robustness during high-speed cornering on tight turns. Compared with standard tube-based approaches, the proposed itube-CILQR algorithm reduces system conservatism and exhibits higher computational speed. Numerical simulations and vision-based experiments were conducted to examine the feasibility of using the proposed algorithm for controlling autonomous vehicles. The results indicated that the proposed algorithm achieved superior vehicle lane-keeping performance to variational CILQRbased methods and model predictive control (MPC) approaches involving the use of a classical interior-point optimizer. Specifically, itube-CILQR required an average runtime of 3.45 ms to generate a control signal for guiding a self-driving vehicle. By comparison, itube-MPC typically required a 4.32 times longer computation time to complete the same task. Moreover, the influence of conservatism on system behavior was investigated by exploring the variations in the interpolation variables derived using the proposed itube-CILQR algorithm during lane-keeping maneuvers.

Merely pursuing performance may adversely affect safety, while a conservative policy for safe exploration will degrade the performance. How to guarantee both safety and performance in learning-based control problems is an interesting yet challenging issue. This paper aims to enhance system performance with a safety guarantee by solving reinforcement learning (RL)-based optimal control problems for nonlinear systems subject to high-relative-degree state constraints and unknown time-varying disturbance/actuator faults. A new type of control barrier functions (CBFs), termed high-order reciprocal-based control barrier function, is proposed to handle high-relative-degree constraints, which extends the design of CBFs to enforce robust safety without knowing the disturbance bound. The concept of gradient similarity is proposed to quantify the relationship between safety and performance. Finally, gradient manipulation and adaptive mechanisms are introduced in the model-based safe RL framework to enhance the performance with a safety guarantee. Two simulation examples illustrate the efficacy of the proposed algorithms.

Reach-Avoid-Stay (RAS) tasks are essential in applications where systems must safely reach a target set and remain within it under all bounded disturbances. Existing approaches either struggle to compute the maximal robust RAS set, the set of all states from which the RAS task is achievable, or are limited in handling general dynamic systems. To address these challenges, this paper proposes a two-step deep reinforcement learning framework that jointly learns the maximal robust RAS set and the corresponding control policy. The first step identifies the maximal robust control-invariant set within the target set and derives a policy that ensures the system remains within it. The second step computes the maximal robust reach-avoid (RA) set using this invariant set as the target, and it is proven that this RA set is equivalent to the maximal robust RAS set. Leveraging this result, a switching policy is constructed from the two step-wise policies, which constitutes a valid policy guaranteeing completion of the RAS task. Simulation results demonstrate that the proposed framework (1) computes the exact maximal robust RAS set in the absence of training errors, yielding the least restrictive RAS policy, and (2) identifies the RAS set with high accuracy while outperforming baseline methods on RAS tasks.

We propose a framework for training neural network controllers with certified robust forward invariant polytopes. First, we parameterize a family of lifted control systems in a higher dimensional space, where the original neural controlled system evolves on an invariant subspace of each lifted system. We use interval analysis and neural network verifiers to further construct a family of lifted embedding systems, carefully capturing the knowledge of this invariant subspace. If the vector field of any lifted embedding system satisfies a sign constraint at a single point, then a certain convex polytope of the original system is robustly forward invariant. Treating the neural network controller and the lifted system parameters as variables, we propose an algorithm to train controllers with certified forward invariant polytopes in the closed-loop control system. Through two examples, we demonstrate how the simplicity of the sign constraint allows our approach to scale with system dimension to over $50$ states, and outperform state-of-the-art Lyapunov-based sampling approaches in runtime.