We consider the problem of optimal control for partially observed dynamical systems. Despite its prevalence in practical applications, there are still very few algorithms available, which take uncertainties in the current state estimates and future observations into account. In other words, most current approaches separate state estimation from the optimal control problem. In this paper, we extend the popular ensemble Kalman filter to receding horizon optimal control problems in the spirit of nonlinear model predictive control. We provide an interacting particle approximation to the forward-backward stochastic differential equations arising from Pontryagin's maximum principle with the forward stochastic differential equation provided by the time-continuous ensemble Kalman-Bucy filter equations. The receding horizon control laws are approximated as linear and are continuously updated as in nonlinear model predictive control. We illustrate the performance of the proposed methodology for an inverted pendulum example.

Abstract-- In this paper, we present an approach for controlling a team of agile fixed-wing aerial vehicles in close proximity to one another. Our approach relies on recedinghorizon nonlinear model predictive control (NMPC) to plan maneuvers across an expanded flight envelope to enable interagent collision avoidance. To facilitate robust collision avoidance and characterize the likelihood of inter-agent collisions, we compute a statistical bound on the probability of the system leaving a tube around the planned nominal trajectory. Finally, we propose a metric for evaluating highly dynamic swarms and use this metric to evaluate our approach. We successfully demonstrated our approach through both simulation and hardware experiments, and to our knowledge, this the first time close-quarters swarming has been achieved with physical aerobatic fixed-wing vehicles.

Accurate trajectory tracking is an essential characteristic for the safe navigation of a quadrotor in cluttered or disturbed environments. In this paper, we present in detail two state-of-the-art model-based control frameworks for trajectory tracking: the Linear Model Predictive Controller (LMPC) and the Nonlinear Model Predictive Controller (NMPC). Additionally, the kinematic and dynamic models of the quadrotor are comprehensively described. Finally, a simulation system is implemented to verify feasibility, demonstrating the effectiveness of both controllers.

We study a real-time iteration (RTI) scheme for solving online optimization problem appeared in nonlinear optimal control. The proposed RTI scheme modifies the existing RTI-based model predictive control (MPC) algorithm, by selecting the stepsize of each Newton step at each sampling time using a differentiable exact augmented Lagrangian. The scheme can adaptively select the penalty parameters of augmented Lagrangian on the fly, which are shown to be stabilized after certain time periods. We prove under generic assumptions that, by involving stepsize selection instead of always using a full Newton step (like what most of the existing RTIs do), the scheme converges globally: for any initial point, the KKT residuals of the subproblems converge to zero. A key step is to show that augmented Lagrangian keeps decreasing as horizon moves forward.

The recent promises of Model Predictive Control in robotics have motivated the development of tailored second-order methods to solve optimal control problems efficiently. While those methods benefit from strong convergence properties, tailored efficient implementations are challenging to derive. In this work, we study the potential effectiveness of first-order methods and show on a torque controlled manipulator that they can equal the performances of second-order methods.

This paper presents a novel approach to automated drifting with a standard passenger vehicle, which involves a Nonlinear Model Predictive Control to stabilise and maintain the vehicle at high sideslip angle conditions. The proposed controller architecture is split into three components. The first part consists of the offline computed equilibrium maps, which provide the equilibrium points for each vehicle state given the desired sideslip angle and radius of the path. The second is the predictive controller minimising the errors between the equilibrium and actual vehicle states. The third is a path-following controller, which reduces the path error, altering the equilibrium curvature path. In a high-fidelity simulation environment, we validate the controller architecture capacity to stabilise the vehicle in automated drifting along a desired path, with a maximal lateral path deviation of 1 m. In the experiments with a standard passenger vehicle, we demonstrate that the proposed approach is capable of bringing and maintaining the vehicle at the desired 30 deg sideslip angle in both high and low friction conditions.

In this paper, we present a novel Reduced Robustified NMPC (R$^2$NMPC) algorithm that has the same complexity as an equivalent nominal NMPC while enhancing it with robustified constraints based on the dynamics of ellipsoidal uncertainty sets. This promises both a closed-loop- and constraint satisfaction performance equivalent to common Robustified NMPC approaches, while drastically reducing the computational complexity. The main idea lies in approximating the ellipsoidal uncertainty sets propagation over the prediction horizon with the system dynamics' sensitivities inferred from the last optimal control problem (OCP) solution, and similarly for the gradients to robustify the constraints. Thus, we do not require the decision variables related to the uncertainty propagation within the OCP, rendering it computationally tractable. Next, we illustrate the real-time control capabilities of our algorithm in handling a complex, high-dimensional, and highly nonlinear system, namely the trajectory following of an autonomous passenger vehicle modeled with a dynamic nonlinear single-track model. Our experimental findings, alongside a comparative assessment against other Robust NMPC approaches, affirm the robustness of our method in effectively tracking an optimal racetrack trajectory while satisfying the nonlinear constraints. This performance is achieved while fully utilizing the vehicle's interface limits, even at high speeds of up to 37.5m/s, and successfully managing state estimation disturbances. Remarkably, our approach maintains a mean solving frequency of 144Hz.

Flexible robots may overcome some of the industry's major challenges, such as enabling intrinsically safe human-robot collaboration and achieving a higher load-to-mass ratio. However, controlling flexible robots is complicated due to their complex dynamics, which include oscillatory behavior and a high-dimensional state space. NMPC offers an effective means to control such robots, but its extensive computational demands often limit its application in real-time scenarios. To enable fast control of flexible robots, we propose a framework for a safe approximation of NMPC using imitation learning and a predictive safety filter. Our framework significantly reduces computation time while incurring a slight loss in performance. Compared to NMPC, our framework shows more than a eightfold improvement in computation time when controlling a three-dimensional flexible robot arm in simulation, all while guaranteeing safety constraints. Notably, our approach outperforms conventional reinforcement learning methods. The development of fast and safe approximate NMPC holds the potential to accelerate the adoption of flexible robots in industry.

Nonlinear Model Predictive Control (NMPC) is a state-of-the-art approach for locomotion and manipulation which leverages trajectory optimization at each control step. While the performance of this approach is computationally bounded, implementations of direct trajectory optimization that use iterative methods to solve the underlying moderately-large and sparse linear systems, are a natural fit for parallel hardware acceleration. In this work, we introduce MPCGPU, a GPU-accelerated, real-time NMPC solver that leverages an accelerated preconditioned conjugate gradient (PCG) linear system solver at its core. We show that MPCGPU increases the scalability and real-time performance of NMPC, solving larger problems, at faster rates. In particular, for tracking tasks using the Kuka IIWA manipulator, MPCGPU is able to scale to kilohertz control rates with trajectories as long as 512 knot points. This is driven by a custom PCG solver which outperforms state-of-the-art, CPU-based, linear system solvers by at least 10x for a majority of solves and 3.6x on average.

Model reduction using Koopman theory as well as the related dynamic mode decomposition (Schmid, 2010), Computationally tractable models are a main requirement build on a lift-and-project concept and aim to construct linear for real-time NMPC (Marquardt, 2002). Data-driven nonintrusive representations of nonlinear dynamics through (nonlinear) model reduction comprises a class of model-free coordinate transformation. Applied Koopman theory has methods for producing low-order representations of highorder a system-theoretic foundation and naturally combines simple dynamical systems from data, e.g., Antoulas et al. dynamic forms with data-driven identification of coordinate (2017). Similar to classical model reduction approaches transformations, e.g., through Kernel methods (Williams (Marquardt, 2002), these data-driven methods project a highorder et al., 2015), deep learning (Lusch et al., 2018), or sparse regression system from the full state space to a lower dimensional techniques (Brunton et al., 2016).