Thomas Brunsch

Adaptive support for patient-cooperative gait rehabilitation with the Lokomat

The rehabilitation robot Lokomat allows automated treadmill training for patients with neurological gait disorders. The basic position control approach for the robot has been extended to patient-cooperative strategies. These strategies provide more freedom and allow patients to actively influence their training. However, patients are likely to need additional support during patient-cooperative training. In this paper, we propose an algorithm based on iterative learning control that shapes a supportive torque field. The torque field is supposed to assist the patient as much as needed in performing the desired task. We evaluated the algorithm in a proof-of-concept experiment with 3 healthy subjects. Results showed that the amount of support was automatically adapted to the activity and the individual needs of the subjects. Furthermore, the support improved the performance of the subjects.

Duality and interval analysis over idempotent semirings

Abstract In this paper semirings with an idempotent addition are considered. These algebraic structures are endowed with a partial order. This allows to consider residuated maps to solve systems of inequalities A ⊗ X ⪯ B (see [3] ). The purpose of this paper is to consider a dual product, denoted ⊙ , and the dual residuation of matrices, in order to solve the following inequality A ⊗ X ⪯ X ⪯ B ⊙ X . Sufficient conditions ensuring the existence of a non-linear projector in the solution set are proposed. The results are extended to semirings of intervals such as they were introduced in [25] .

Control of Cyclically Operated High-Throughput Screening Systems

Abstract In previous work we have shown how (max, +)-algebra can be used to model cyclically operated high-throughput screening systems. In this paper the system is modeled in a two-dimensional dioid M ax in [γ, δ]. A controller is determined using residuation theory. The resulting control guarantees just-in-time operation of the plant. A small example is used to demonstrate the approach to model and control HTS systems. To apply the determined controller, it is rewritten in terms of counter -functions. A simulation of the system with and without controller is given and results are discussed.

Discrete-event systems model of an outbreak response

During an outbreak of an infectious disease the public health unit has several strategies which can be imposed to contain the spread of the disease. In order to do so it is necessary to evaluate the efficiency of different response policies according to the specific setting of the outbreak. In this work we present a new approach to model such infectious disease outbreaks using discrete-event systems. This approach allows us to adapt the system easily to specific settings or new diseases. Thus, using our model the health units would be able to determine an optimal response to a threatening outbreak.

Max-Plus Algebraic Modeling and Control of High-Throughput Screening Systems

In this paper, we present a max-plus algebraic model for cyclically operated high-throughput screening plants. A max-plus algebraic representation of the system, derived directly from a discrete-event systems model of the predetermined globally optimal solution, contains negative order arcs, forcing certain events in previous cycles to occur after events in the current cycle. With respect to the cycle index, though of course not in terms of time, the model is acausal. However, the model can be transformed into a system representation without negative order arcs. The obtained max-plus algebraic model can then be applied as a controller to handle unexpected deviations from the predetermined cyclic operation during runtime.

Modeling and control of high-throughput screening systems in a max-plus algebraic setting

In this paper, we present a max-plus algebraic modeling and control approach for cyclically operated high-throughput screening plants. In previous work an algorithm has been developed to determine the globally optimal solution of the cyclic scheduling problem. The obtained optimal schedule is modeled in a max-plus algebraic framework. The max-plus algebraic model can then be used to generate appropriate control actions to handle unexpected deviations from the predetermined cyclic operation during runtime.

Max-Plus Algebraic Modeling and Control of High-Throughput Screening Systems with Multi-Capacity Resources

Abstract In previous work we have shown how a max-plus algebraic model can be derived for cyclically operated high-throughput screening systems and how such a model can be used to design a controller to handle unexpected deviations from the predetermined cyclic operation during runtime. In this paper, we introduce an extension of this approach for high-throughput screening systems containing multi-capacity resources, i.e., resources that can handle more than one activity at the same time.

Discrete-event systems in a dioid framework : Control theory

In this chapter, we will recall contributions to dioid theory dealing with control that were achieved during the last two decades. Just like in classical control engineering, control is to be understood as having an action on the inputs so as to adapt to given specifications. For instance, one could aim at finding an optimal control in order to track an a priori known output trajectory. Since inversion, which would be necessary for such a computation, does not exist in general in a dioid framework, we will also present notions of residuation theory, which introduces pseudo-inverses that are suitable to our needs. Provided a model of a system and a specified output for it, it can be shown that there exists a greatest input that leads to an output which is lower than or equal to the specified one. In practice, this greatest solution implies that all the events occur as late as possible while ensuring that the output events occur before the ones given by the specified output. In a production management context, this comes down to delaying as much as possible the input of raw parts in the manufacturing system, while ensuring a predefined throughput; hence the internal stock is reduced as much as possible. The control strategy is then optimal according to the just-in-time criterion. This chapter will provide the results allowing to synthesize this optimal control. But this kind of open-loop strategy does not take the real-time response of the system into account. So we will also extend control strategies to closed-loop ones, which allow to react to possible disturbances. For each control strategy an illustrative example dealing with a High-Throughput Screening system, which has served as a case study within the DISC project, will be given.

Stock Reduction for Timed Event Graphs Based on Output Feedback

Abstract In timed event graphs (TEG), stock represents the number of tokens present in the system. It is very similar to work-in-process for manufacturing systems. In general, when choosing a feedback controller, a compromise is sought between fastness of the system and stock size. The classical choice in the (max, +) literature consists in reducing the stock as much as possible without delaying the output. In this paper, the constraint is weakened: the response of the controlled system to a specific, predefined reference input w must be as fast as the one of the uncontrolled system, but may be slower for other inputs. In return, lower stock is expected. After formally defining this new controller, its performance in terms of stock is compared with the one of the classical controller. This last part relies heavily on second order theory for TEG.

Patient-Cooperative Control: Adapting Robotic Interventions to Individual Human Capabilities

Patient-cooperative control strategies aim at improving the efficacy of current rehabilitation robots. The key aspects of these strategies are the transparency of the robots, constraints for safety and guidance, and individual interventions. Within the frame of transparency and constraints, interventions of challenging or facilitating nature can be applied. In this paper, we propose a way of providing facilitating interventions by force fields or global parameters, which are adapted by iterative learning control. We evaluate this approach in two scenarios with the rehabilitation robot Lokomat; first, to assist knee extension during stance phase, and second, to modulate how actively human subjects participate in bearing their own body weight. Both examples show that iterative learning control algorithms provide a feasible way to allow patients to train at a continuously challenging level according to their individual capabilities.