A robust iterative learning control for continuous-time nonlinear systems with disturbances

In this paper, we study the trajectory tracking problem using iterative learning control for continuous-time nonlinear systems with a generic fixed relative degree in the presence of disturbances. This class of controllers iteratively refine the control input relying on the tracking error of the previous trials and some properly tuned learning gains. Sufficient conditions on these gains guarantee the monotonic convergence of the iterative process. However, the choice of the gains is heuristically hand-tuned given an approximated system model and no information on the disturbances. Thus, in the cases of inaccurate knowledge of the model or iteration-varying measurement errors, external disturbances, and delays, the convergence condition is unlikely to be verified at every iteration. To overcome this issue, we propose a robust convergence condition, which ensures the applicability of the pure feedforward control even if other classical conditions are not fulfilled for some trials due to the presence of disturbances. Furthermore, we quantify the upper bound of the nonrepetitive disturbance that the iterative algorithm is able to handle. Finally, we validate the convergence condition simulating the dynamics of a two degrees of freedom underactuated arm with elastic joints, where one is active, and the other is passive, and a Franka Emika Panda manipulator

Elastic Structure Preserving Control for Compliant Robots Driven by Agonistic-Antagonistic Actuators (ESPaa)

The regulation of the link positions of compliant robots, damping out undesired link oscillations while preserving the system's inherent elasticity is still a challenging task in practical applications. This task becomes even harder to be tackled in the case of compliant robots driven by agonistic-antagonistic variable stiffness actuators in which there are two motors associated with each joint of the system. In this work, leveraging on the physical realization of the elastic mechanism of such actuators, we propose a novel control law able to simultaneously achieve a good regulation performance and a desired damped behavior at the link, while preserving the elastic structure of the system as well as the possibility of adjusting the passive stiffness at the joints. Simulations on the agonistic-antagonistic actuators of the forearm and wrist joints of the Hand Arm System from the German Aerospace Center (DLR) and experiments on a planar platform with an analogous actuation unit, namely qbMove Advanced, validate the proposed method

Overcoming the Torque/Stiffness Range Tradeoff in Antagonistic Variable Stiffness Actuators

To face the demand for applications in which robots have to safely interact with humans and the environment, the research community developed new types of actuators with compliant characteristics. To embody compliance into the actuator, elastic elements with fixed or variable compliance can be used. Among the variable stiffness mechanisms, a popular approach is based on the agonistic-antagonistic (A-A) layout, where two prime movers are elastically connected to the output shaft of the actuator. Notwithstanding the conceptually simple realization of the A-A layout, one limitation is that, due to the nonlinear torque/deflection characteristic of the elastic transmissions and to the limited spring elongation, the stiffness range achievable at the output shaft reduces as the external torque increases. In this work, a novel layout, based on the A-A principle, is proposed to increase the torque/stiffness capability of the actuator. To achieve this result, we combine elastic transmissions with linear and nonlinear torque/deflection characteristics. The mathematical model of the new layout and a possible implementation are analyzed. Then, the design of a novel variable stiffness actuator is presented and experimental validations are shown to compare the new device with the benchmark

Trajectory tracking of a one-link flexible arm via iterative learning control

Trajectory tracking of flexible link robots is a classical control problem. Historically, the link elasticity was considered as something to be removed. Hence, the control performance was guaranteed by adopting high-gain feedback loops and, possibly, a dynamic compensation with the result to stiffen up the dynamic behavior of the robot. Nowadays, robots are pushed more and more towards a safe physical interaction with a less and less structured environment. Hence, the design and control of the robots moved to an on-purpose introduction of highly compliant elements in the robot bodies, the so-called soft robotics, and towards control approaches that aim to provide the tracking performance without a substantial change in the robot dynamic behavior. Following this approach, we present an iterative learning control that relies mainly on a feedforward component, hence preserves the robot dynamics, for trajectory tracking of a one-link flexible arm. We provide a condition, based on the system dynamics and similar to the Strong Inertially Coupled property, that ensures the applicability of the proposed control method. Finally, we report simulation and experimental tests to validate the theoretical results

Iterative Learning Control for Compliant Underactuated Arms

Operations involving safe interactions in unstructured environments require robots with adapting behaviors. Compliant manipulators are a promising technology to achieve this goal. Despite that, some classical control problems such as following a trajectory are still open. A typical solution is to compensate the system dynamics with feedback loops. However, this solution increases the effective robot stiffness and jeopardizes the safety property provided by the compliant design. On the other hand, purely feedforward approaches can achieve good tracking performance while preserving the robot intrinsic compliance. However, a feedforward control framework for robots with passive elastic joints is still missing. This article presents an iterative learning control algorithm for purely feedforward trajectory tracking for compliant underactuated arms. Each arm is composed of active elastic joints and a generic number of passive ones connected through rigid links. We prove the convergence of the iterative method, also in the presence of uncertainties and bounded disturbances. Different output functions are analyzed providing conditions, based on the system inertial properties that ensure the algorithm applicability. Additionally, an automatic selection of the learning gain is proposed. Finally, we extensively validate the theoretical results with simulations and experiments

Modelación de la fase termofílica en un proceso de composteo

En la actualidad existe una elevada generación de desechos orgánicos y otros por distintas industrias, estos desechos requieren de procesos controlados y lugares adecuados para su óptimo tratamiento. El composteo, que se basa en la degradación aerobia de materia orgánica a CO2, NH3+ y H2O con la generación de calor, es una de las técnicas más utilizadas en la actualidad para el tratamiento de desechos orgánicos. En este bioproceso existe una interrelación entre los parámetros físicos, químicos y biológicos. Dentro de los parámetros físicos el más importante es la temperatura ya que este parámetro determina el desarrollo de comunidades microbianas específicas, que a su vez permite la degradación de la materia orgánica y con la generación de calor se obtiene la eliminación de patógenos. Además, la eficiencia del bioproceso recae sobre un buen desarrollo de la fase termofílica. Por lo que el presente trabajo tuvo como objetivo modelar la fase termofílica en pilas de composta de diferentes dimensiones: 0.5m (PC1), 1m (PC2), 1.5m (PC3), 2m (PC4). La fase termofílica duró 24, 51, 101 y >153 días, las Tmax (° C) fueron de 62.7, 76.2, 75.5 y 66.1 para las pilas PC1, PC2, PC3 y PC4, respectivamente. A partir de la ecuación de transferencia de calor de Fourier se obtuvieron parámetros globales de difusión y generación de calor, con la ecuación de balance de energía se modeló perfiles de temperatura en diferentes puntos para pilas de composta de diferentes dimensiones. Finalmente, los resultados del presente trabajo muestran que el dimensionamiento de pilas de composta afecta la duración e intensidad (Tmax) de la fase termofílica durante un proceso de composteo. La distribución de temperaturas y la zona más caliente dentro de una pila de composta es diferente y cambia en el transcurso del tiempo. La duración e intensidad de la fase termofilica se ve afectada también: a) por la cantidad de materia orgánica, b) por los gradientes de humedad y densidad dentro de la pila y c) por la difusividad de calor desde la superficie de la pila hasta el medio ambiente. Abstract Nowadays high organic waste is generated and others by different industries. These wastes require controlled processes and suitable locations for its optimum treatment. Currently composting, an aerobic process where organic matter is converted to CO2, NH3 +, H2O with heat generation, is one of the most common techniques used for the treatment of organic waste. Within this bioprocess physical, chemical and biological parameters interrelate. Temperature is the most important physical parameter because it allows the development of specific microbial communities, which in turn allows the degradation of organic matter and the heat generated allows the elimination of pathogens. Furthermore, the efficiency of this bioprocess lies on a good thermophilic phase. Moreover, this study aimed to model the thermophilic phase in composting piles of different dimensions. The thermophilic phase lasted 24, 51, 101 and >153 days for piles PC1, PC2, PC3 and PC4, respectively. The Tmax (° C) were 62.7, 76.2, 75.5 and 66.1 for piles PC1, PC2, PC3 and PC4, respectively. Temperature profiles were modeled in different points by using Fourier’s heat transfer equation. The size of a compost pile affects the duration and intensity (Tmax) of the thermophilic phase during the composting process. The temperature distribution and the hottest area within a compost pile is different and changes over time. The duration and intensity of the thermophilic phase is also affected by: a) the amount of organic matter, b) the density and humidity gradients within the pile and c) the heat diffusivity coefficient obtained from the surface of the pile to the environment. Finally, Fourier’s heat transfer equation allowed to obtain parameters such as: heat diffusivity coefficient and heat generation, which were useful to the development of temperature profiles in compost piles of different dimensions

Time Generalization of Trajectories Learned on Articulated Soft Robots

To avoid feedback-related stiffening of articulated soft robots, a substantive feedforward contribution is crucial. However, obtaining reliable feedforward actions requires very accurate models, which are not always available for soft robots. Learning-based approaches are a promising solution to the problem. They proved to be an effective strategy achieving good tracking performance, while preserving the system intrinsic compliance. Nevertheless, learning methods require rich data sets, and issues of scalability and generalization still remain to be solved. This letter proposes a method to generalize learned control actions to execute a desired trajectory with different velocities - with the ultimate goal of making these learning-based architectures sample efficient. More specifically we prove that the knowledge of how to execute a same trajectory at five different speeds is necessary and sufficient to execute the same trajectory at any velocity - without any knowledge of the model. We also give a simple constructive way to calculate this new feedforward action. The effectiveness of the proposed technique is validated in extensive simulation on a Baxter robot with soft springs playing a drum, and experimentally on a VSA double pendulum performing swinging motions