In this paper, we present an extension to the recursive Gaussian Process (RGP) regression that enables the satisfaction of inequality constraints and is well suited for a real-time execution in control applications. The soft inequality constraints are integrated by introducing an additional extended Kalman Filter (EKF) update step using pseudo-measurements. The sequential formulation of the algorithm and several developed heuristics ensure both the performance and a low computational effort of the algorithm. A special focus lies on an efficient consideration of monotonicity assumptions for GPs in the form of inequality constraints. The algorithm is statistically validated in simulations, where the possible advantages in comparison with the standard RGP algorithm become obvious. The paper is concluded with a successful experimental validation of the developed algorithm for the monotonicity-preserving learning of heat transfer values for the control of a vapor compression cycle evaporator, leveraging a previously published partial input output linearization (IOL).

In this paper, the focus is on ice clamping of workpieces using feedback-controlled Peltier cells, which represents a novel nonlinear control application. As only the hot-side temperature is accessible for measurements, an Unscented Kalman filter (UKF) estimates the temperatures on both the hot and cold sides of the Peltier element and a lumped disturbance heat flow acting on the cold side. These estimates are employed in linearized discrete-time model predictive control (MPC), which is adapted in each time step based on Taylor linearizations around desired trajectories, also considering the predicted future linearization errors, and tracks a given cold-side temperature profile despite interfering heat inflow from the machining process. Here, the nonlinear system model is exploited to calculate favorable desired values that correspond to low currents, minimizing the overall energy consumption and avoiding another possible operating point with high currents. The achieved tracking precision and estimation accuracy is pointed out in simulation results for a typical ice clamping scenario subject to disturbances.

Parallelization and vectorization strategies play a key role in accelerating the training of Deep Reinforcement Learning agents, for example by utilizing several agents simultaneously or by operating multiple independent training environments in parallel. Focusing on the latter approach, this work investigates the impact of Vectorized Environments on the training speed and performance for a collision-free path planning task with the seven-degree-of-freedom Franka Research 3 robotic manipulator. Using the model-free, off-policy Reinforcement Learning algorithm Twin Delayed Deep Deterministic Policy Gradient, the results show a tremendous potential for improving the overall performance and reducing the wall-clock training time when collecting experiences from multiple different environments at the same time. As it can be seen, a simultaneous increase of the mini-batch size can lead to more generalized agents and an improved training stability. Finally, the effect of true parallelization, i.e., distributing the individual environments onto separate workers on the work station, is illustrated, proving an option for an even further training speed-up.

In many applications of robotic path planning, several obstacles must be avoided simultaneously while their relative importance for collision avoidance may vary over time. By pure intuition, obstacles that are of major importance in the current time step shall be respected more strictly to avoid potential collisions. Using the model-free, actor-critic Reinforcement Learning algorithm Twin Delayed Deep Deterministic Policy Gradient, the impact of a dynamically sorted environmental state description for collision-free path planning tasks incorporating multiple obstacles with the 7 degrees of freedom Franka Research 3 robotic manipulator is investigated. The influence of this approach is analyzed in a sensitivity analysis of the trained actor network, where the determined allocation of the network’s input state vector is found to have significant impact onto the action selection. The training results further indicate a tremendous benefit when consistently sorting the state vector during operation according to the minimum Euclidean distances of the obstacles to the robot.

As the drive force depends in a nonlinear manner on the currents, an accurate tracking control of permanent magnet linear motors is challenging. In this paper, a cascaded control is proposed and combined with a recursive estimator. In the inner loop of the cascaded structure, an inversion-based control design is employed in combination with an eigenvalue assignment. The outer loop involves a backstepping tracking control of the armature position, where a nonlinear error dynamics is assigned. Given nonlinear friction and other disturbances, a lumped disturbance force is estimated by a dual Kalman filter – in addition to the state variables. This combination achieves a high robustness of the overall control structure. The control performance is investigated in detailed simulations, where also measurement noise and external disturbances are included.

Hydro-mechanical transmissions are employed in many vehicle applications due to their advantage of a continuously variable transmission ratio. The main issue in their deployment, however, is a precise control of the hydrostatic unit within this system, whose characteristics are highly nonlinear and affected by unknown disturbances. Many control concepts for such transmissions have already been proposed, including both model-based and model-free approaches. In this paper, the design and simulation results are presented for a discrete-time version of Generalized Proportional Integral (GPI) control applied to the hydrostatic unit of a hydro-mechanical transmission. In contrast to previous work, the motor volumetric displacement is constant, which leads to a single-input single output (SISO) control approach. The discrete-time GPI controller can be easily implemented on an electronic control unit (ECU) and outperforms a classical PID control in a comparison. Simulation results using a validated system model from previous research indicate a promising tracking performance.

This paper proposes a general control approach for first-order input-affine systems of arbitrary finite system order. The control scheme, which is based on an inversion of the system dynamics in combination with an adaptation of the reference values, guarantees close-to-optimal tracking of systems with input constraints. After the presentation of the control scheme for the SISO case, stability, performance and robustness properties are investigated. Then, a first application in the form of a cooling cycle is presented in which the proposed approach shows a nearly identical performance to an alternative offline optimisation. The control scheme is extended to MIMO systems by means of a prioritization of outputs and an online solution of linear programming problems. For this scenario, a nonlinear real-world example is discussed in the form of a vapor compression cycle. The achieved performance of the control scheme is demonstrated by simulation results.

This paper presents an innovative model-based control approach of a vapor compression cycle, which relies on a partial input-output linearisation (IOL) for a nonlinear feedback control of the evaporator outlet enthalpy. First, the test rig and the corresponding control-oriented system model are presented. For the inner control loop, the IOL is derived and used for the design of a nonlinear feedback control. Moreover, different extensions are discussed, among them an integral error feedback by means of the heat transfer value and a nonlinear stabilizing feedback control. For the control of the coolant outlet temperature in the outer loop, a PI-controller in combination with an inversion-based feedforward control is employed. The partial IOL-control is tested separately, and the effects of the adaptations are compared in experiments on the test rig. Here, the integral feedback by means of the heat-transfer value improves the control performance significantly, whereas the nonlinear stabilizing feedback contributes to a reduction of the necessary control effort. The overall control approach is validated experimentally on the test rig. Especially the partial IOL-control in the inner loop provides very promising results.

This paper proposes an estimator-based tracking control for a thermoelectric cooling system with Peltier cells. It is intended for use in a novel manufacturing system leveraging ice clamping. Starting from physical principles and conservation equations, a 4th-order state space model is developed and exploited within an input-output linearization, where the internal dynamics can be shown to be asymptotically stable. A backstepping-based tracking control is designed to accurately track the desired cold side temperature even in the presence of disturbances. Unknown states and disturbances are observed using an Unscented Kalman Filter, which outperforms previous results with alternative estimators. Conclusive simulation results are discussed and demonstrate the performance of the combined control and estimation structure.

This paper demonstrates the usage of Deep Reinforcement Learning to learn an optimal swing-up-strategy for a pneumatically actuated variable-length pendulum. For this purpose, the model-free algorithm Deep-Q-Networks is applied inside a virtual environment. Here, the influence of different reward strategies on the training success is analysed, separating between intuitive and more sophisticated functions that use pre-existing domain knowledge. The impact of the used reward function was found to be significant as the agent’s performance could be improved tremendously by inducing pre-existing knowledge about physical effects into the reward strategy.

In robotic path planning tasks, Reinforcement Learning agents typically receive global or relative Euclidean coordinates, e.g., with respect to a target reference point as direct state information. Nevertheless, a more egocentric view of the environment seems to be favorable – based on information in polar or spherical coordinates about objects surrounding the robot. Using the model-free, actor-critic algorithm Twin Delayed Deep Deterministic Policy Gradient in combination with Prioritized Experience Replay, the advantages of an alternative definition of states using egocentric TCP-coordinates is evaluated and compared in simulations to classical approaches within two typical environments. The training results indicate a tremendous potential of the egocentric state space definition that not only offers faster learning but also more successful trainings.

This paper deals with the evaluation of point clouds measured by a 2D Lidar system aiming at the detection and description of corner features. Here, the extraction of walls using the robust RANSAC algorithm serves as a basic pillar for the detection of corners within the operating area of the Lidar system. To ensure the recognizability and persistence of the detected corners, an innovative approach is presented that creates individual descriptors for single corners. The developed techniques have been experimentally investigated and validated with a Lidar system in a realistic indoor test scenario.

Teleoperation deals with extraordinary situations where an external operator takes over the control of an autonomous vehicle. Especially in complex urban scenarios, this may cause a too high workload for the human operator, resulting in suboptimal solutions. This contribution presents a teleoperation paradigm to raise the autonomy level of teleoperated driving, while the operator still remains the main decision-maker in all driving tasks. The introduced approach generates collision-free paths using LiDAR sensor information and suggests them to the operator. Therefore, a new hybrid path planning method has been developed, which searches and clusters in the first phase all feasible paths in the environment using a modified Rapidly-Exploring-Random Tree (RRT). In the second phase, the path selected by the operator is optimized online by a modified CHOMP algorithm. Real driving experiments confirm the effectiveness of the approach and highlight both the achieved driving safety and real time capability.

This paper presents the design and a comparison of two cascaded control schemes based on nonlinear model predictive controllers (NMPC) for the position control of a pneumatic actuator. Both control schemes consist of a NMPC for the pneumatic subsystem while the outer mechanical subsystem is in one case controlled by a NMPC as well, and in the other case by a state-feedback controller (LQR). To cope with the high impact of nonlinear friction, a feedforward friction compensation is employed, and the mechanical subsystem is extended by an integrator. The control approaches are implemented on a test rig consisting of a double-acting pneumatic cylinder actuated by a single 5/3-proportional valve using the GRAMPC-toolbox. Based on experimental results on the test rig it can be shown that both controllers achieve a precise position tracking for different desired trajectories.

This paper presents a sliding-mode approach for the robust tracking control of the body-fixed velocities of an underactuated hovercraft vehicle. Pontryagin’s Maximum Principle is applied for an optimal trajectory planning – providing optimal state and input variables for feedforward control. Moreover, the design-related cross-couplings of the two control inputs are analysed and addressed by a heuristic approach. The performance of the proposed nonlinear control structure is investigated by simulations using an identified model of a corresponding experimental vehicle.

This paper deals with the optimization of velocity trajectories for railway vehicles w.r.t. the total energy consumption between two successive stops. Based on four principle operating modes - acceleration, cruising, coasting, and braking - energy-optimal trajectories are computed by optimizing the sequence of operating modes as well as the corresponding switching points. The optimization involves two consecutive steps: As a basic technique in the first step, a multimodal optimization, namely the Firefly Algorithm (FFA), is utilized to determine the boundaries defined by the timetable request regarding both time and position constraints. In a second step, the energy-optimal solution will be determined within the remaining parameter space reduced by the first step. The advantages of this approach are pointed out by detailed simulation results.

This paper presents a model-based approach to an energy-optimal speed control of a centrifugal pump that is used within heating systems for buildings. The pump operating strategy is based on two main pillars. The first pillar is represented by a module that provides an estimation of the unknown flow resistances in the hydraulic circuit of the heating system. The second pillar is given by a detailed model-based analysis of the pump characteristic in combination with an optimization approach regarding the energy-efficiency to determine the optimal angular velocity of the hydraulic pump. The resulting control strategy is applied to a validated detailed simulation model, which addresses a generic but typical heating scenario. It becomes obvious that a significant improvement w.r.t. the state-of-the-art is achieved.

A significant barrier regarding a successful implementation of fenceless robot cells into manufacturing areas with humans is given by the inefficiency due to safety requirements. Robot motions have to be slowed down so that an unexpected collision with a human does not result in human injuries. This velocity reduction leads to longer cycle times and, hence, fenceless robot cells turn out as uneconomic. In this paper, a new approach for human-robot collaboration in assembly tasks is presented. For a better performance of the robot, methods are investigated on how the robot can exploit a maximum performance while maintaining the safety of collaborating humans. For this purpose, the kinematics and dynamics of a human arm are described by a control-oriented dynamic model to determine its capability and reachability. Successful experiments validate the dynamic model as well as a corresponding projection approach for calculating possible movements of the human arm that may lead to a collision with the robot. Finally, this information is used to calculate an admissible path velocity that minimizes the danger of human injuries.

In this paper, a Takagi-Sugeno (TS) approach is proposed for the position control of a hydraulic servo cylinder. Based on a nonlinear mathematical model of the test rig, an exact quasi-linear model with state-dependent matrices is derived and reformulated as a TS fuzzy model. In this framework, the given lower and upper bounds of the nonlinearities are considered by separate local models belonging to a polytope. The adaptive feedback control gains are given by a weighted combination of those of the corner models. To improve the position tracking behaviour, the TS control structure is extended by feedforward control actions as well as an observer-based disturbance compensation. Here, a lumped disturbance force - consisting of imperfections of the feedforward friction model and parameter uncertainty - is estimated by a reduced-order nonlinear observer. The benefits of the proposed control structure and the achieved control performance are shown by experimental results from an implementation on a test rig.

In this paper, a decentralised control approach for an innovative 5 MW wind turbine with a hydrostatic transmission is presented that covers the whole range from low to very high wind speeds. An active damping of tower oscillations is achieved by using the pitch angle as control input. An elastic multibody system is employed to derive a control-oriented model for the first tower bending mode, which serves for the design of a stabilising control law. The active oscillation damping is combined with a multi-variable gain-scheduled PI state feedback control that allows for tracking desired trajectories for the angular velocities of both rotor and generator. The overall control performance is illustrated by realistic simulation results, which show an improved damping of tower oscillations and excellent tracking behaviour for the controlled variables.

A cascaded control strategy for an innovative Duo-copter test rig - a helicopter with two rotors combined with a guiding mechanism - is presented in this paper. The guiding mechanism consists of a rocker arm with a sliding carriage that enforces a planar workspace. The Duocopter is attached to the carriage by a rotary joint and offers 3 degrees of freedom. The derived system model has similarities with a planar model of a quadrotor but involves additional terms due to the guiding mechanism. A gain-scheduled cascaded control strategy using extended linearisation is proposed: an outer MIMO control loop is responsible for the nonlinear control of both the horizontal and the vertical Duocopter positions, whereas the rotation angle of the Duocopter is controlled in a linear inner control loop. An additional feedforward control takes into account known parts of the coupling forces between the carriage and the rocker. The control structure is extended by a sliding mode observer (SMO) that provides estimates for the state vector and, moreover, estimates for remaining errors concerning the feedforward coupling forces. The sum of the feedforward part and the estimated part can be used to robustly and accurately compensate for the impact of the guiding mechanism on the motion of the Duocopter frame. Thereby, an excellent tracking performance in vertical and horizontal directions can be achieved. The efficiency of the proposed control strategy is demonstrated by experiments.

In this paper, a robust nonlinear control approach based on a simplified control-oriented model of an engine cooling system for vehicles is presented. An electrically driven radiator fan is considered as a control input. Based on the system description, a second-order sliding mode control is proposed to track desired trajectories of the engine outlet temperature. The second-order sliding mode control provides a smooth control action and reduces the chattering phenomenon with the introduction of a first-order time derivative of the sliding manifold. A gain-scheduled modified Utkin sliding mode observer, which uses both an output error feedback and a switching term, is employed to estimate unknown heat flows within the system. The estimated heat flows are used in the control design in order to compensate the disturbances acting on the system. An experimental analysis highlights the effectiveness of the second-order sliding mode control in combination with a sliding mode based observer design.

This paper presents a comparison of two alternative control structures for an active oscillation damping of truck drive trains. Uncomfortable oscillations in the drive train may occur in phases when the dry clutch is slipping. The negative friction coefficient of the clutch lining could cause an undesired judder, which leads to a severe driver discomfort. At first, a control-oriented model is derived by a step-by-step simplification. The first control design consists of a model-based approach that uses a feedback of the relative angular velocity for a reduction of the oscillation amplitudes. Despite a measurement of the angular velocity at the drive side, this value is usually not available for the transmission control unit. Therefore, a modified Utkin sliding mode observer is employed that estimates the state vector as well as a disturbance torque. In the second approach, a simple feedback of the angular velocity signal at the clutch side is used for an active damping of torsional oscillations in the truck drive train. Both control approaches are validated at a dedicated test rig at the Chair of Mechatronics, University of Rostock.

In this paper, a multi-variable nonlinear control of a twin rotor aerodynamical system (TRAS) is presented. A control-oriented state-space model with four states is derived employing Lagrange's equations. Using this system representation, a multi-variable flatness-based control is designed for an accurate trajectory tracking concerning both the pitch angle characterising the vertical motion and the azimuth angle related to the horizontal motion. Due to unmeasurable states as well as disturbance torques affecting the pitch axis and the azimuth axis, a discrete-time Extended Kalman Filter (EKF) is employed and combined with a discrete-time implementation of the multi-variable flatness-based control. The effectiveness of the proposed control strategy is highlighted by experimental results from a test rig that show an excellent tracking behaviour.

A cascaded control strategy for an innovative Duocopter test stand - a helicopter with two rotors combined with a guiding mechanism - is presented in this paper. The guiding mechanism consists of a rocker arm with a sliding carriage that enforces a planar workspace of the Duocopter. The Duocopter is connected to the carriage by a rotary joint and offers 3 degrees of freedom. The derived system model has similarities with a PVTOL and a planar model of a quadrocopter but involves additional terms due to the guiding mechanism. In the paper, a model-based cascaded control strategy is proposed: the outer MIMO control loop is given by the inverted system model to control the horizontal and the vertical Duocopter position with a nonlinear error dynamics derived from backstepping techniques. The rotation angle of the Duocopter is controlled in a linear inner control loop of high bandwidth. Due to uncertain system parameters and reasonable simplifications at the modelling of the test stand, the control structure is extended by an unscented Kalman filter. Thereby, an excellent tracking performance in vertical and horizontal direction can be achieved. The efficiency of the proposed control strategy is demonstrated by both simulations and experiments.

For a horizontal-axis wind turbine (HAWT), a dynamic nonlinear model with four degrees of freedom is derived and transformed into a Takagi-Sugeno (TS) model structure using the sector nonlinearity approach. Thereby, an exact transformation of the nonlinear model is obtained as a weighted combination of linear models. This structure allows for a convenient design of controller and observer structures. The maps of the rotor thrust and torque coefficients can be implemented in the model as look-up tables or, alternatively, as analytical nonlinear functions. Open-loop simulation results of the derived TS model for a reference model turbine are compared to those obtained with the aero-elastic code FAST. The small deviations obtained demonstrate the high model quality of the control-oriented TS model. In future work, the derived TS model shall be used as a basis for the design of fault detection and isolation (FDI) concepts.