Erkan Kayacan

Vedant Bhandari, Erkan Kayacan

This paper demonstrates the applicability of the combination of concurrent learning as a tool for parameter estimation and non-parametric Gaussian Process for online disturbance learning. A control law is developed by using both techniques sequentially in the context of feedback linearization. The concurrent learning algorithm estimates the system parameters of structured uncertainty without requiring persistent excitation, which are used in the design of the feedback linearization law. Then, a non-parametric Gaussian Process learns unstructured uncertainty. The closed-loop system stability for the nth-order system is proven using the Lyapunov stability theorem. The simulation results show that the tracking error is minimized (i) when true values of model parameters have not been provided, (ii) in the presence of disturbances introduced once the parameters have converged to their true values and (iii) when system parameters have not converged to their true values in the presence of disturbances.

Erkan Kayacan, Erdal Kayacan, Herman Ramon et al.

This paper addresses the trajectory tracking problem of an autonomous tractor-trailer system by using a fast distributed nonlinear model predictive control algorithm in combination with nonlinear moving horizon estimation for the state and parameter estimation in which constraints on the inputs and the states can be incorporated. The proposed control algorithm is capable of driving the tractor-trailer system to any desired trajectory ensuring high control accuracy and robustness against environmental disturbances.

Erkan Kayacan, Erdal Kayacan, Herman Ramon et al.

As a model is only an abstraction of the real system, unmodeled dynamics, parameter variations, and disturbances can result in poor performance of a conventional controller based on this model. In such cases, a conventional controller cannot remain well tuned. This paper presents the control of a spherical rolling robot by using an adaptive neuro-fuzzy controller in combination with a sliding-mode control (SMC)-theory-based learning algorithm. The proposed control structure consists of a neuro-fuzzy network and a conventional controller which is used to guarantee the asymptotic stability of the system in a compact space. The parameter updating rules of the neuro-fuzzy system using SMC theory are derived, and the stability of the learning is proven using a Lyapunov function. The simulation results show that the control scheme with the proposed SMC-theory-based learning algorithm is able to not only eliminate the steady-state error but also improve the transient response performance of the spherical rolling robot without knowing its dynamic equations.

Erkan Kayacan, Erdal Kayacan, Herman Ramon et al.

More efficient agricultural machinery is needed as agricultural areas become more limited and energy and labor costs increase. To increase their efficiency, trajectory tracking problem of an autonomous tractor, as an agricultural production machine, has been investigated in this study. As a widely used model-based approach, model predictive control is preferred in this paper to control the yaw dynamics of the tractor which can deal with the constraints on the states and the actuators in a system. The yaw dynamics is identified by using nonlinear least squares frequency domain system identification. The speed is controlled by a proportional-integral-derivative controller and a kinematic trajectory controller is used to calculate the desired speed and the desired yaw rate signals for the subsystems in order to minimize the tracking errors in both the longitudinal and transversal directions. The experimental results show the accuracy and the efficiency of the proposed control scheme in which the euclidean error is below $40$ cm for time-based straight line trajectories and $60$ cm for time-based curved line trajectories, respectively.

Erdal Kayacan, Erkan Kayacan, Herman Ramon et al.

Provision of some autonomous functions to an agricultural vehicle would lighten the job of the operator but in doing so, the accuracy should not be lost to still obtain an optimal yield. Autonomous navigation of an agricultural vehicle involves the control of different dynamic subsystems, such as the yaw angle dynamics and the longitudinal speed dynamics. In this study, a proportional-integral-derivative controller is used to control the longitudinal velocity of the tractor. For the control of the yaw angle dynamics, a proportional-derivative controller works in parallel with a type-2 fuzzy neural network. In such an arrangement, the former ensures the stability of the related subsystem, while the latter learns the system dynamics and becomes the leading controller. In this way, instead of modeling the interactions between the subsystems prior to the design of model-based control, we develop a control algorithm which learns the interactions online from the measured feedback error. In addition to the control of the stated subsystems, a kinematic controller is needed to correct the errors in both the x- and the y- axis for the trajectory tracking problem of the tractor. To demonstrate the real-time abilities of the proposed control scheme, an autonomous tractor is equipped with the use of reasonably priced sensors and actuators. Experimental results show the efficacy and efficiency of the proposed learning algorithm.

Erkan Kayacan, Erdal Kayacan, Herman Ramon et al.

This paper addresses the trajectory tracking problem of an autonomous tractor-trailer system by using a decentralized control approach. A fully decentralized model predictive controller is designed in which interactions between subsystems are neglected and assumed to be perturbations to each other. In order to have a robust design, a tube-based approach is proposed to handle the differences between the nominal model and real system. Nonlinear moving horizon estimation is used for the state and parameter estimation after each new measurement, and the estimated values are fed to robust tube-based decentralized nonlinear model predictive controller. The proposed control scheme is capable of driving the tractor-trailer system to any desired trajectory ensuring high control accuracy and robustness against neglected subsystem interactions and environmental disturbances. The experimental results show an accurate trajectory tracking performance on a bumpy grass field.

Erkan Kayacan, Erdal Kayacan, Mojtaba Ahmadieh Khanesar

In order to achieve faster and more robust convergence (especially under noisy working environments), a sliding mode theory-based learning algorithm has been proposed to tune both the premise and consequent parts of type-2 fuzzy neural networks in this paper. Differently from recent studies, where sliding mode control theory-based rules are proposed for only the consequent part of the network, the developed algorithm applies fully sliding mode parameter update rules for both the premise and consequent parts of the type-2 fuzzy neural networks. In addition, the responsible parameter for sharing the contributions of the lower and upper parts of the type-2 fuzzy membership functions is also tuned. Moreover, the learning rate of the network is updated during the online training. The stability of the proposed learning algorithm has been proved by using an appropriate Lyapunov function. Several comparisons have been realized and shown that the proposed algorithm has faster convergence speed than the existing methods such as gradient-based and swarm intelligence-based methods. Moreover, the proposed learning algorithm has a closed form, and it is easier to implement than the other existing methods.

Erkan Kayacan, Herman Ramon, Wouter Saeys

This paper proposes a new robust trajectory tracking error-based control approach for unmanned ground vehicles. A trajectory tracking error-based model is used to design a linear model predictive controller and its control action is combined with feedforward and robust control actions. The experimental results show that the proposed control structure is capable to let a tractor-trailer system track both linear and curvilinear target trajectories with low tracking error.

Erkan Kayacan, Wouter Saeys, Herman Ramon et al.

This paper focuses on the trajectory tracking control problem for an articulated unmanned ground vehicle. We propose and compare two approaches in terms of performance and computational complexity. The first uses a nonlinear mathematical model derived from first principles and combines a nonlinear model predictive controller (NMPC) with a nonlinear moving horizon estimator (NMHE) to produce a control strategy. The second is based on an input-state linearization (ISL) of the original model followed by linear model predictive control (LMPC). A fast real-time iteration scheme is proposed, implemented for the NMHE-NMPC framework and benchmarked against the ISL-LMPC framework, which is a traditional and cheap method. The experimental results for a time-based trajectory show that the NMHE-NMPC framework with the proposed real-time iteration scheme gives better trajectory tracking performance than the ISL-LMPC framework and the required computation time is feasible for real-time applications. Moreover, the ISL-LMPC produces results of a quality comparable to the NMHE-NMPC framework at a significantly reduced computational cost.

Erkan Kayacan, Sierra N. Young, Joshua M. Peschel et al.

Accurate steering through crop rows that avoids crop damage is one of the most important tasks for agricultural robots utilized in various field operations, such as monitoring, mechanical weeding, or spraying. In practice, varying soil conditions can result in off-track navigation due to unknown traction coefficients so that it can cause crop damage. To address this problem, this paper presents the development, application, and experimental results of a real-time receding horizon estimation and control (RHEC) framework applied to a fully autonomous mobile robotic platform to increase its steering accuracy. Recent advances in cheap and fast microprocessors, as well as advances in solution methods for nonlinear optimization problems, have made nonlinear receding horizon control (RHC) and receding horizon estimation (RHE) methods suitable for field robots that require high frequency (milliseconds) updates. A real-time RHEC framework is developed and applied to a fully autonomous mobile robotic platform designed by the authors for in-field phenotyping applications in Sorghum fields. Nonlinear RHE is used to estimate constrained states and parameters, and nonlinear RHC is designed based on an adaptive system model which contains time-varying parameters. The capabilities of the real-time RHEC framework are verified experimentally, and the results show an accurate tracking performance on a bumpy and wet soil field. The mean values of the Euclidean error and required computation time of the RHEC framework are respectively equal to $0.0423$ m and $0.88$ milliseconds.

Erkan Kayacan, Girish Chowdhary

This paper presents a Tracking-Error Learning Control (TELC) algorithm for precise mobile robot path tracking in off-road terrain. In traditional tracking error-based control approaches, feedback and feedforward controllers are designed based on the nominal model which cannot capture the uncertainties, disturbances and changing working conditions so that they cannot ensure precise path tracking performance in the outdoor environment. In TELC algorithm, the feedforward control actions are updated by using the tracking error dynamics and the plant-model mismatch problem is thus discarded. Therefore, the feedforward controller gradually eliminates the feedback controller from the control of the system once the mobile robot has been on-track. In addition to the proof of the stability, it is proven that the cost functions do not have local minima so that the coefficients in TELC algorithm guarantee that the global minimum is reached. The experimental results show that the TELC algorithm results in better path tracking performance than the traditional tracking error-based control method. The mobile robot controlled by TELC algorithm can track a target path precisely with less than $10$ cm error in off-road terrain.

Zhongzhong Zhang, Erkan Kayacan, Benjamin Thompson et al.

This paper presents high precision control and deep learning-based corn stand counting algorithms for a low-cost, ultra-compact 3D printed and autonomous field robot for agricultural operations. Currently, plant traits, such as emergence rate, biomass, vigor, and stand counting, are measured manually. This is highly labor-intensive and prone to errors. The robot, termed TerraSentia, is designed to automate the measurement of plant traits for efficient phenotyping as an alternative to manual measurements. In this paper, we formulate a Nonlinear Moving Horizon Estimator (NMHE) that identifies key terrain parameters using onboard robot sensors and a learning-based Nonlinear Model Predictive Control (NMPC) that ensures high precision path tracking in the presence of unknown wheel-terrain interaction. Moreover, we develop a machine vision algorithm designed to enable an ultra-compact ground robot to count corn stands by driving through the fields autonomously. The algorithm leverages a deep network to detect corn plants in images, and a visual tracking model to re-identify detected objects at different time steps. We collected data from 53 corn plots in various fields for corn plants around 14 days after emergence (stage V3 - V4). The robot predictions have agreed well with the ground truth with $C_{robot}=1.02 \times C_{human}-0.86$ and a correlation coefficient $R=0.96$. The mean relative error given by the algorithm is $-3.78\%$, and the standard deviation is $6.76\%$. These results indicate a first and significant step towards autonomous robot-based real-time phenotyping using low-cost, ultra-compact ground robots for corn and potentially other crops.

Erkan Kayacan

This paper addresses to Sliding Mode Learning Control (SMLC) of uncertain nonlinear systems with Lyapunov stability analysis. In the control scheme, a conventional control term is used to provide the system stability in compact space while a Type-2 Neuro-Fuzzy Controller (T2NFC) learns system behavior so that the T2NFC takes the overall control of the system completely in a very short time period. The stability of the sliding mode learning algorithm was proven in literature; however, it is so restrictive for systems without the overall system stability. To address this shortcoming, a novel control structure with a novel sliding surface is proposed in this paper and the stability of the overall system is proven for nth-order uncertain nonlinear systems. To investigate the capability and effectiveness of the proposed learning and control algorithms, the simulation studies have been achieved under noisy conditions. The simulation results confirm that the developed SMLC algorithm can learn the system behavior in the absence of any mathematical model knowledge and exhibit robust control performance against external disturbances.

Erkan Kayacan

This paper develops a Closed-Loop Error Learning Control (CLELC) algorithm for feedback linearizable systems with experimental validation on a mobile robot. Traditional feedback and feedforward controllers are designed based on the nominal model by using Feedback Linearization Control (FLC) method. Then, an intelligent controller is designed based on sliding mode learning algorithm that utilizes closed-loop error dynamics to learn the system behavior. The controllers are working in parallel, and the intelligent controller can gradually replace the feedback controller from the control of the system. In addition to the stability of the sliding mode learning algorithm, the closed-loop stability of an $n$th order feedback linearizable system is proven. The simulation results demonstrate that CLELC algorithm can improve control performance (e.g., smaller rise time, settling time and overshoot) in the absence of uncertainties, and also provides robust control performance in the presence of uncertainties as compared to traditional FLC method. To test the efficiency and efficacy of CLELC algorithm, the trajectory tracking problem of a tracked mobile robot is studied in real-time. The experimental results demonstrate that CLELC algorithm ensures high-accurate trajectory tracking performance than traditional FLC method.