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Book Review: Discrete-time Markov control processes: Basic optimality criteria

Fast feedback control and safety guarantees are essential in modern robotics. We present an approach that achieves both by combining novel robust model predictive control (MPC) with function approximation via (deep) neural networks (NNs). The result is a new approach for complex tasks with nonlinear, uncertain, and constrained dynamics as are common in robotics. Specifically, we leverage recent results in MPC research to propose a new robust setpoint tracking MPC algorithm, which achieves reliable and safe tracking of a dynamic setpoint while guaranteeing stability and constraint satisfaction. The presented robust MPC scheme constitutes a one-layer approach that unifies the often separated planning and control layers, by directly computing the control command based on a reference and possibly obstacle positions. As a separate contribution, we show how the computation time of the MPC can be drastically reduced by approximating the MPC law with a NN controller. The NN is trained and validated from offline samples of the MPC, yielding statistical guarantees, and used in lieu thereof at run time. Our experiments on a state-of-the-art robot manipulator are the first to show that both the proposed robust and approximate MPC schemes scale to real-world robotic systems.

Safe and Fast Tracking on a Robot Manipulator: Robust MPC and Neural Network Control.

Coupled simulation of thermally active building systems to support a digital twin

We study the application of a data-enabled predictive control (DeePC) algorithm for position control of real-world nano-quadcopters. The DeePC algorithm is a finite-horizon, optimal control method that uses input/output measurements from the system to predict future trajectories without the need for system identification or state estimation. The algorithm predicts future trajectories of the quadcopter by linearly combining previously measured trajectories (motion primitives). We illustrate the necessity of a regularized variant of the DeePC algorithm to handle the nonlinear nature of the real-world quadcopter dynamics with noisy measurements. Simulation-based analysis is used to gain insights into the effects of regularization, and experimental results validate that these insights carry over to the real-world quadcopter. Moreover, we demonstrate the reliability of the DeePC algorithm by collecting a new set of input/output measurements for every real-world experiment performed. The performance of the DeePC algorithm is compared to Model Predictive Control based on a first-principles model of the quadcopter. The results are demonstrated with a video of successful trajectory tracking of the real-world quadcopter.

Data-enabled predictive control for quadcopters

Most industrial robots are not capable of teaching by hand and require path points to be specified by teaching pendants. To enable the teaching of industrial robots by hand without any force sensors, this paper proposes a scheme to minimize the external force estimation error and reduce disturbance in the guiding task by using the virtual mass and virtual friction model. In this case, the maximum velocity and acceleration of the robot end effector shall be limited to ensure safety. Thus, the operator is allowed to guide the robot by hand. The joint torque is obtained from the motor current. The inertial force and friction of the links and driving systems are analyzed. The nonlinear dynamic model of the industrial robot is built and its parameters are calibrated by a nonlinear method. The force estimation is referenced to set the virtual friction and to design the force-following controller. Hence the end effector can follow the direction of external force compliantly and suppress jitters. Finally, several experiments on a six degrees of freedom industrial robot demonstrate the validity of the proposed control scheme.

A Sensorless Hand Guiding Scheme Based on Model Identification and Control for Industrial Robot

Parameter Identification of the KUKA LBR iiwa Robot Including Constraints on Physical Feasibility

We propose a simple and computationally efficient approach for designing a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The uncertainty is modeled as an additive disturbance and an additive error on the system dynamics matrices. Set based bounds for each component of the model uncertainty are assumed to be known. We separate the constraint tightening strategy into two parts, depending on the length of the MPC horizon. For a horizon length of one, the robust MPC problem is solved exactly, whereas for other horizon lengths, the model uncertainty is over-approximated with a net-additive component. The resulting MPC controller guarantees robust satisfaction of state and input constraints in closed-loop with the uncertain system. With appropriately designed terminal components and an adaptive horizon strategy, we prove the controller's recursive feasibility and stability of the origin. With numerical simulations, we demonstrate that our proposed approach gains up to 15x online computation speedup over a tube MPC strategy, while stabilizing about 98% of the latter's region of attraction.

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A Simple Robust MPC for Linear Systems with Parametric and Additive Uncertainty

Active control of a rod-net formwork system prototype

We propose a novel approach to design a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The uncertain system is modeled as linear parameter varying with additive disturbance. Set bounds for the system matrices and the additive uncertainty are assumed to be known. We formulate a novel optimization-based constraint tightening strategy around a predicted nominal trajectory which utilizes these bounds. With an appropriately designed terminal cost function and constraint set, we prove robust satisfaction of the imposed constraints by the resulting MPC in closed-loop with the uncertain system, and Input to State Stability of the origin. We highlight the efficacy of our proposed approach via a numerical example.

Robust MPC for LTI Systems with Parametric and Additive Uncertainty: A Novel Constraint Tightening Approach.

This article presents scalable controller synthesis methods for heterogeneous and partially heterogeneous systems. First, heterogeneous systems composed of different subsystems that are interconnected over a directed graph are considered. Techniques from robust and gain-scheduled controller synthesis are employed, in particular, the full-block S-procedure, to deal with the decentralized system part in a nominal condition and with the interconnection part in a multiplier condition. Under some structural assumptions, we can decompose the synthesis conditions into conditions that are the size of the individual subsystems. To solve these decomposed synthesis conditions that are coupled only over neighboring subsystems, we propose a distributed method based on the alternating direction method of multipliers. It only requires nearest-neighbor communication and no central coordination is needed. Then, a new classification of systems is introduced that consists of groups of homogeneous subsystems with different interconnection types. This classification includes heterogeneous systems as the most general and homogeneous systems as the most specific case. Based on this classification, we show how the interconnected system model and the decomposed synthesis conditions can be formulated in a more compact way. The computational scalability of the presented methods with respect to a growing number of subsystems and interconnections is analyzed, and the results are demonstrated in numerical examples.

Yvonne R. Stürz

Papers

Parameter Identification of the KUKA LBR iiwa Robot Including Constraints on Physical Feasibility

A Simple Robust MPC for Linear Systems with Parametric and Additive Uncertainty

Active control of a rod-net formwork system prototype

Robust MPC for LTI Systems with Parametric and Additive Uncertainty: A Novel Constraint Tightening Approach.

Distributed Control Design for Heterogeneous Interconnected Systems