Abstract-In this paper, a framework for Nonlinear Model Predictive Control (NMPC) for heavily noise-affected systems is presented. Within this framework, the noise influence, which originates from uncertainties during model identification or measurement, is explicitly considered. This leads to a significant increase in the control quality. One part of the proposed framework is the efficient state prediction, which is necessary for NMPC. It is based on transition density approximation by hybrid transition densities, which allows efficient closed-form state prediction of time-variant nonlinear systems with continuous state spaces in discrete time. Another part of the framework is a versatile value function representation using Gaussian mixtures, Dirac mixtures, and even a combination of both. Based on these methods, an efficient closed-form algorithm for calculating an approximate value function of the NMPC optimal control problem employing dynamic programming is presented. Thus, also very long optimization horizons can be used and furthermore it is possible to calculate the value function off-line, which reduces the on-line computational burden significantly. The capabilities of the framework and especially the benefits that can be gained by incorporating the noise in the controller are illustrated by the example of a miniature walking robot following a given path.

Abstract-Model identification and measurement acquisition is always to some degree uncertain. Therefore, a framework for Nonlinear Model Predictive Control (NMPC) is proposed that explicitly considers the noise influence on nonlinear dynamic systems with continuous state spaces and a finite set of control inputs in order to significantly increase the control quality. Integral parts of NMPC are the prediction of system states over a finite horizon as well as the problem specific modeling of reward functions. For achieving an efficient and also accurate state prediction, the introduced framework uses transition densities approximated by means of axis-aligned Gaussian mixtures. The representation power of Gaussian mixtures is also used to model versatile reward functions. Thus, together with the prediction technique a closed-form calculation of the optimization problems arising from NMPC is possible. Additionally, an efficient algorithm for calculating an approximate value function of the corresponding optimal control problem employing dynamic programming is presented. Thus, the value function can be calculated off-line, which reduces the on-line computational burden significantly and also permits the use of long optimization horizons. The capabilities of the framework and especially the benefits that can be gained by incorporating the noise in the controller are illustrated by the example of a two-wheeled differential-drive mobile robot following a given path.

Abstract-In this paper, an approach to the finite-horizon optimal state-feedback control problem of nonlinear, stochastic, discrete-time systems is presented. Starting from the dynamic programming equation, the value function will be approximated by means of Taylor series expansion up to second-order derivatives. Moreover, the problem will be reformulated, such that a minimum principle can be applied to the stochastic problem. Employing this minimum principle, the optimal control problem can be rewritten as a two-point boundary-value problem to be solved at each time step of a shrinking horizon. To avoid numerical problems, the two-point boundary-value problem will be solved by means of a continuation method. Thus, the curse of dimensionality of dynamic programming is avoided, and good candidates for the optimal state-feedback controls are obtained. The proposed approach will be evaluated by means of a scalar example system.

Abstract-In many technical systems, the system state, which is to be controlled, is not directly accessible, but has to be estimated from observations. Furthermore, the uncertainties arising from this procedure are typically neglected in the controller. To remedy this deficiency, in this paper, we present a novel approach to stochastic nonlinear model predictive control (NMPC) for heavily noise-affected systems with not directly accessible, i.e., hidden states, extending the stochastic NMPCframework presented in [1]. An important property of our novel method is that, in contrast to classical approaches, time-variant system and measurement equations as well as time-variant step rewards can be considered. Extending the techniques from [1] by introducing virtual future observations and combining this with a novel tree search algorithm, called probabilistic branch-and-bound search (PBAB), a solution with a feasible computational demand of the challenging problem is possible.

Abstract-For the collaborative control of a team of robots, a set of well-suited high-level control algorithms, especially for path planning and measurement scheduling, is essential. The quality of these control algorithms can be significantly increased by considering uncertainties that arise, e.g. from noisy measurements or system model abstraction, by incorporating stochastic filters into the control. To develop these kinds of algorithms and to prove their effectiveness, obviously realworld experiments with real world uncertainties are mandatory. Therefore, a test-environment for evaluating algorithms for collaborative control of a team of robots is presented. This test-environment is founded on miniature walking robots with six degrees of freedom. Their novel locomotion concept not only allows them to move in a wide variety of different motion patterns far beyond the possibilities of traditionally employed wheel-based robots, but also to handle real-world conditions like uneven ground or small obstacles. These robots are embedded in a modular test-environment, comprising infrastructure and simulation modules as well as a high-level control module with submodules for pose estimation, path planning, and measurement scheduling. The interaction of the individual modules of the introduced test-environment is illustrated by an experiment from the field of cooperative localization with focus on measurement scheduling, where the robots that perform distance measurements are selected based on a novel criterion, the normalized mutual Mahalanobis distance.