Model-Based Control Using Koopman Operators

This paper explores the application of Koopman operator theory to the control of robotic systems. The operator is introduced as a method to generate data-driven models that have utility for model-based control methods. We then motivate the use of the Koopman operator towards augmenting model-based control. Specifically, we illustrate how the operator can be used to obtain a linearizable data-driven model for an unknown dynamical process that is useful for model-based control synthesis. Simulated results show that with increasing complexity in the choice of the basis functions, a closed-loop controller is able to invert and stabilize a cart- and VTOL-pendulum systems. Furthermore, the specification of the basis function are shown to be of importance when generating a Koopman operator for specific robotic systems. Experimental results with the Sphero SPRK robot explore the utility of the Koopman operator in a reduced state representation setting where increased complexity in the basis function improve open- and closed-loop controller performance in various terrains, including sand.Comment: 8 page

Adaptive model based control for wastewater treatment plants

In biological wastewater treatment, nitrogen and phosphorous are removed by activated sludge. The process requires oxygen input via aeration of the activated sludge tank. Aeration is responsible for about 60% of the energy consumption of a treatment plant. Hence optimization of aeration can contribute considerably to the increase of energy-efficiency in wastewater treatment. To this end, we introduce an adaptive model based control strategy for aeration called adaptive WOMBAT. The strategy is an improvement of the original WOMBAT, which has been successfully implemented at wastewater treatment plant Westpoort in Amsterdam. In this paper we propose to improve the physics-based model by introducing automatic parameter adaptation. In an experimental model setup the adaptive model based control algorithm proves to result in better effluent quality with less energy consumption. Moreover, it is able to react to the varying circumstances of a real treatment plant and can, therefore, operate without human supervision

Propagation Networks for Model-Based Control Under Partial Observation

There has been an increasing interest in learning dynamics simulators for model-based control. Compared with off-the-shelf physics engines, a learnable simulator can quickly adapt to unseen objects, scenes, and tasks. However, existing models like interaction networks only work for fully observable systems; they also only consider pairwise interactions within a single time step, both restricting their use in practical systems. We introduce Propagation Networks (PropNet), a differentiable, learnable dynamics model that handles partially observable scenarios and enables instantaneous propagation of signals beyond pairwise interactions. Experiments show that our propagation networks not only outperform current learnable physics engines in forward simulation, but also achieve superior performance on various control tasks. Compared with existing model-free deep reinforcement learning algorithms, model-based control with propagation networks is more accurate, efficient, and generalizable to new, partially observable scenes and tasks.Comment: Accepted to ICRA 2019. Project Page: http://propnet.csail.mit.edu Video: https://youtu.be/ZAxHXegkz4

Application of model based control to robotic manipulators

A robot that can duplicate humam motion capabilities in such activities as balancing, reaching, lifting, and moving has been built and tested. These capabilities are achieved through the use of real time Model-Based Control (MBC) techniques which have recently been demonstrated. MBC accounts for all manipulator inertial forces and provides stable manipulator motion control even at high speeds. To effectively demonstrate the unique capabilities of MBC, an experimental robotic manipulator was constructed, which stands upright, balancing on a two wheel base. The mathematical modeling of dynamics inherent in MBC permit the control system to perform functions that are impossible with conventional non-model based methods. These capabilities include: (1) Stable control at all speeds of operation; (2) Operations requiring dynamic stability such as balancing; (3) Detection and monitoring of applied forces without the use of load sensors; (4) Manipulator safing via detection of abnormal loads. The full potential of MBC has yet to be realized. The experiments performed for this research are only an indication of the potential applications. MBC has no inherent stability limitations and its range of applicability is limited only by the attainable sampling rate, modeling accuracy, and sensor resolution. Manipulators could be designed to operate at the highest speed mechanically attainable without being limited by control inadequacies. Manipulators capable of operating many times faster than current machines would certainly increase productivity for many tasks

Model based control strategies for a class of nonlinear mechanical sub-systems

This paper presents a comparison between various control strategies for a class of mechanical actuators common in heavy-duty industry. Typical actuator components are hydraulic or pneumatic elements with static non-linearities, which are commonly referred to as Hammerstein systems. Such static non-linearities may vary in time as a function of the load and hence classical inverse-model based control strategies may deliver sub-optimal performance. This paper investigates the ability of advanced model based control strategies to satisfy a tolerance interval for position error values, overshoot and settling time specifications. Due to the presence of static non-linearity requiring changing direction of movement, control effort is also evaluated in terms of zero crossing frequency (up-down or left-right movement). Simulation and experimental data from a lab setup suggest that sliding mode control is able to improve global performance parameters