This letter presents an approach to guaranteed trajectory tracking for nonlinear control-affine systems subject to external disturbances based on robust control contraction metrics (CCM) that aims to minimize the $\mathcal {L}_\infty$ gain from the disturbances to nominal-actual trajectory deviations. The guarantee is in the form of invariant tubes, computed offline and valid for any nominal trajectories, in which the actual states and inputs of the system are guaranteed to stay despite disturbances. Under mild assumptions, we prove that the proposed robust CCM (RCCM) approach yields tighter tubes than an existing approach based on CCM and input-to-state stability analysis. We show how the RCCM-based tracking controller together with tubes can be incorporated into a feedback motion planning framework to plan safe trajectories for robotic systems. Simulation results illustrate the effectiveness of the proposed method and empirically demonstrate reduced conservatism compared to the CCM-based approach.

Quadrotors that can operate predictably in the presence of imperfect model knowledge and external disturbances are crucial in safety-critical applications. We present $\boldsymbol {\mathcal {L}}_{1}$ Quad, a control architecture that ensures uniformly bounded transient response of the quadrotor’s uncertain dynamics on the special Euclidean group SE(3). By leveraging the geometric controller and the $\boldsymbol {\mathcal {L}}_{1}$ adaptive controller, the $\boldsymbol {\mathcal {L}}_{1}$ Quad architecture provides a theoretically justified framework for the design and analysis of quadrotor’s tracking controller in the presence of nonlinear (time- and state-dependent) uncertainties on both the translational and rotational dynamics. In addition, we validate the performance of the $\boldsymbol {\mathcal {L}}_{1}$ Quad architecture through extensive experiments for 11 types of uncertainties across various trajectories. The results demonstrate that the $\boldsymbol {\mathcal {L}}_{1}$ Quad can achieve consistently small tracking errors despite the uncertainties and disturbances and significantly outperforms existing state-of-the-art controllers.

We propose a unified framework to instantly generate a safe optimal control action for a new task from existing controllers on multi-agent systems (MASs). The control action composition is achieved by taking a weighted mixture of the existing controllers according to the contribution of each component task. Instead of sophisticatedly tuning the cost parameters and other hyper-parameters for safe and reliable behavior in the optimal control framework, the safety of each single task solution is guaranteed using the control barrier functions (CBFs) for high relative degree stochastic systems, which constrains the system state within a known safe operation region where it originates from. Linearity of CBF constraints in control ensures the feasibility of safe control action composition. The discussed framework can immediately provide reliable solutions to new tasks by taking a weighted mixture of solved component-task actions and satisfying some CBF constraints, instead of performing an extensive sampling to compute a new controller. Our results are verified and demonstrated on both a single UAV and two cooperative UAV teams in an environment with obstacles.

We present a method for the stability analysis of a large class of linear Partial Differential Equations (PDEs) in one spatial dimension. We rely on Lyapunov analysis to establish the exponential stability of the systems under consideration. The proposed test for the verification of the underlying Lyapunov inequalities relies on the existence of solutions of a system of coupled differential equations. We illustrate the application of this method using a PDE actuated by a backstepping computed feedback law. Furthermore, for the case of PDEs defined by polynomial data, we formulate a numerical methodology in the form of a convex optimization problem which can be solved algorithmically. We show the effectiveness of the proposed numerical methodology using examples of different types of PDEs.

This paper presents a contraction-based learning control architecture that allows for using model learning tools to learn matched model uncertainties while guaranteeing trajectory tracking performance during the learning transients. The architecture relies on a disturbance estimator to estimate the pointwise value of the uncertainty, i.e., the discrepancy between a nominal model and the true dynamics, with pre-computable estimation error bounds, and a robust Riemannian energy condition for computing the control signal. Under certain conditions, the controller guarantees exponential trajectory convergence during the learning transients, while learning can improve robustness and facilitate better trajectory planning. Simulation results validate the efficacy of the proposed control architecture.