Fully Actuated Manifold Constraint Based Output Feedback Control for Input-Constrained Uncertain Nonlinear Systems

We present a robust safety-filtering framework for input-constrained underactuated linear systems subject to unknown disturbances. A baseline H-$\infty$ input is derived from a zero-sum differential game, while a disturbance observer supplies an estimate and a transient error bound. The baseline input is adjusted using the disturbance estimate, while the estimate and its error bound are used to define robust high-order control barrier function constraints; forward invariance holds as long as the admissible-input set remains nonempty. For scalar-input systems, pointwise feasibility is determined from an exact input interval, and the interval width defines the feasibility margin. A finite-horizon H-$\infty$ performance balance accounts for the accumulated deviation of the applied input from the baseline H-$\infty$ policy. Simulations on a linearized two-wheeled balancing robot show how position and body-pitch constraints compete for the same bounded wheel-torque input.

Safe navigation in dynamic environments is challenging when system dynamics are unknown and actuator inputs are limited. Existing methods either rely on accurate models, require online optimization, or do not explicitly account for input constraints. This paper presents a real-time control framework for unknown Euler-Lagrange systems that guarantees finite-time reach-avoid-stay (FT-RAS) specifications while respecting actuator limits. We extend the spatiotemporal tube (STT) framework by incorporating input constraints into the controller design and derive offline-verifiable feasibility conditions that relate the available control authority to the tube design and uncertainty bounds. The resulting framework is approximation-free and computationally efficient, making it suitable for real-time implementation. The proposed approach is validated through simulations on a mobile robot, a quadrotor, and a spacecraft, together with hardware experiments on a mobile robot, demonstrating safe navigation while satisfying actuator constraints.

Learning-based control techniques use data from past trajectories to control systems with uncertain dynamics. However, learning-based controllers are often computationally inefficient, limiting their practicality. To address this limitation, we propose a learning-based controller that exploits differential flatness, a property of many robotic systems. Recent research on using flatness for learning-based control either is limited in that it (i) ignores input constraints, (ii) applies only to single-input systems, or (iii) is tailored to specific platforms. In contrast, our approach uses a system extension and block-diagonal cost formulation to control general multi-input, nonlinear, affine systems. Furthermore, it satisfies input and half-space flat state constraints and guarantees probabilistic Lyapunov decrease using only two sequential convex optimizations. We show that our approach performs similarly to, but is multiple times more efficient than, a Gaussian process model predictive controller in simulation, and achieves competitive tracking in real hardware experiments.