Author Archives: Juan-antonio Fernández-madrigal

Value iteration applied in control systems when the model of the plant is substituted by data acquired from the plant

June 27, 2017 08:33 ,

Yongqiang Li, Zhongsheng Hou, Yuanjing Feng, Ronghu Chi, Data-driven approximate value iteration with optimality error bound analysis, Automatica, Volume 78, April 2017, Pages 79-87, ISSN 0005-1098, DOI: 10.1016/j.automatica.2016.12.019.

Features of the data-driven approximate value iteration (AVI) algorithm, proposed in Li et al. (2014) for dealing with the optimal stabilization problem, include that only process data is required and that the estimate of the domain of attraction for the closed-loop is enlarged. However, the controller generated by the data-driven AVI algorithm is an approximate solution for the optimal control problem. In this work, a quantitative analysis result on the error bound between the optimal cost and the cost under the designed controller is given. This error bound is determined by the approximation error of the estimation for the optimal cost and the approximation error of the controller function estimator. The first one is concretely determined by the approximation error of the data-driven dynamic programming (DP) operator to the DP operator and the approximation error of the value function estimator. These three approximation errors are zeros when the data set of the plant is sufficient and infinitely complete, and the number of samples in the interested state space is infinite. This means that the cost under the designed controller equals to the optimal cost when the number of iterations is infinite.

NOTE: Another paper on the same issue in the same journal.

Posted in: Applications of reinforcement learning to control engineering , Tagged: ,

A study of the influence of uncertain, stochastic delays in the stability of LTI SISO systems

June 22, 2017 11:54 ,

T. Qi, J. Zhu and J. Chen, “Fundamental Limits on Uncertain Delays: When Is a Delay System Stabilizable by LTI Controllers?,” in IEEE Transactions on Automatic Control, vol. 62, no. 3, pp. 1314-1328, March 2017. DOI: 10.1109/TAC.2016.2584007.

This paper concerns the stabilization of linear time-invariant (LTI) systems subject to uncertain, possibly time-varying delays. The fundamental issue under investigation, referred to as the delay margin problem, addresses the question: What is the largest range of delay such that there exists a single LTI feedback controller capable of stabilizing all the plants for delays within that range? Drawing upon analytic interpolation and rational approximation techniques, we derive fundamental bounds on the delay margin, within which the delay plant is guaranteed to be stabilizable by a certain LTI output feedback controller. Our contribution is threefold. First, for single-input single-output (SISO) systems with an arbitrary number of plant unstable poles and nonminimum phase zeros, we provide an explicit, computationally efficient bound on the delay margin, which requires computing only the largest real eigenvalue of a constant matrix. Second, for multi-input multi-output (MIMO) systems, we show that estimates on the variation ranges of multiple delays can be obtained by solving LMI problems, and further, by finding bounds on the radius of delay variations. Third, we show that these bounds and estimates can be extended to systems subject to time-varying delays. When specialized to more specific cases, e.g., to plants with one unstable pole but possibly multiple nonminimum phase zeros, our results give rise to analytical expressions exhibiting explicit dependence of the bounds and estimates on the pole and zeros, thus demonstrating how fundamentally unstable poles and nonminimum phase zeros may limit the range of delays over which a plant can be stabilized by a LTI controller.

Posted in: Control Engineering , Tagged: ,

Very efficient global non-linear optimization for real-time robotic problems through the re-use of pre-computed solutions

June 22, 2017 11:22 ,

K. Hauser, “Learning the Problem-Optimum Map: Analysis and Application to Global Optimization in Robotics,” in IEEE Transactions on Robotics, vol. 33, no. 1, pp. 141-152, Feb. 2017. DOI: 10.1109/TRO.2016.2623345.

This paper describes a data-driven framework for approximate global optimization in which precomputed solutions to a sample of problems are retrieved and adapted during online use to solve novel problems. This approach has promise for real-time applications in robotics, since it can produce near globally optimal solutions orders of magnitude faster than standard methods. This paper establishes theoretical conditions on how many and where samples are needed over the space of problems to achieve a given approximation quality. The framework is applied to solve globally optimal collision-free inverse kinematics problems, wherein large solution databases are used to produce near-optimal solutions in a submillisecond time on a standard PC.

Posted in: Mathematics , Tagged:

Varying the number of particles in a PF in order to improve the speed of convergence, with a short related work about adapting the number of particles for other goals

June 22, 2017 10:51 ,

V. Elvira, J. Míguez and P. M. Djurić, “Adapting the Number of Particles in Sequential Monte Carlo Methods Through an Online Scheme for Convergence Assessment,” in IEEE Transactions on Signal Processing, vol. 65, no. 7, pp. 1781-1794, April1, 1 2017. DOI: 10.1109/TSP.2016.2637324.

Particle filters are broadly used to approximate posterior distributions of hidden states in state-space models by means of sets of weighted particles. While the convergence of the filter is guaranteed when the number of particles tends to infinity, the quality of the approximation is usually unknown but strongly dependent on the number of particles. In this paper, we propose a novel method for assessing the convergence of particle filters in an online manner, as well as a simple scheme for the online adaptation of the number of particles based on the convergence assessment. The method is based on a sequential comparison between the actual observations and their predictive probability distributions approximated by the filter. We provide a rigorous theoretical analysis of the proposed methodology and, as an example of its practical use, we present simulations of a simple algorithm for the dynamic and online adaptation of the number of particles during the operation of a particle filter on a stochastic version of the Lorenz 63 system.

Posted in: Bayesian filtering , Tagged:

Qualitative robot navigation

June 22, 2017 10:06 ,

Sergio Miguel-Tomé, Navigation through unknown and dynamic open spaces using topological notions, Connection Science, DOI: 10.1080/09540091.2016.1277691.

Until now, most algorithms used for navigation have had the purpose of directing system towards one point in space. However, humans communicate tasks by specifying spatial relations among elements or places. In addition, the environments in which humans develop their activities are extremely dynamic. The only option that allows for successful navigation in dynamic and unknown environments is making real-time decisions. Therefore, robots capable of collaborating closely with human beings must be able to make decisions based on the local information registered by the sensors and interpret and express spatial relations. Furthermore, when one person is asked to perform a task in an environment, this task is communicated given a category of goals so the person does not need to be supervised. Thus, two problems appear when one wants to create multifunctional robots: how to navigate in dynamic and unknown environments using spatial relations and how to accomplish this without supervision. In this article, a new architecture to address the two cited problems is presented, called the topological qualitative navigation architecture. In previous works, a qualitative heuristic called the heuristic of topological qualitative semantics (HTQS) has been developed to establish and identify spatial relations. However, that heuristic only allows for establishing one spatial relation with a specific object. In contrast, navigation requires a temporal sequence of goals with different objects. The new architecture attains continuous generation of goals and resolves them using HTQS. Thus, the new architecture achieves autonomous navigation in dynamic or unknown open environments.

Posted in: Robot motion planning , Tagged:

A new Kalman Filter that is more robust under certain deviations of the gaussian hypothesis

June 22, 2017 09:46 ,

Badong Chen, Xi Liu, Haiquan Zhao, Jose C. Principe, Maximum correntropy Kalman filter, Automatica, Volume 76, February 2017, Pages 70-77, ISSN 0005-1098, DOI: 10.1016/j.automatica.2016.10.004.

Traditional Kalman filter (KF) is derived under the well-known minimum mean square error (MMSE) criterion, which is optimal under Gaussian assumption. However, when the signals are non-Gaussian, especially when the system is disturbed by some heavy-tailed impulsive noises, the performance of KF will deteriorate seriously. To improve the robustness of KF against impulsive noises, we propose in this work a new Kalman filter, called the maximum correntropy Kalman filter (MCKF), which adopts the robust maximum correntropy criterion (MCC) as the optimality criterion, instead of using the MMSE. Similar to the traditional KF, the state mean vector and covariance matrix propagation equations are used to give prior estimations of the state and covariance matrix in MCKF. A novel fixed-point algorithm is then used to update the posterior estimations. A sufficient condition that guarantees the convergence of the fixed-point algorithm is also given. Illustration examples are presented to demonstrate the effectiveness and robustness of the new algorithm.

Posted in: Bayesian filtering , Tagged: ,

A promising survey on robust estimation methods aimed at robotic applications

June 22, 2017 09:35 ,

Michael Bosse, Gabriel Agamennoni and Igor Gilitschenski (2016), “Robust Estimation and Applications in Robotics”, Foundations and Trends® in Robotics: Vol. 4: No. 4, pp 225-269. DOI: 10.1561/2300000047.

Solving estimation problems is a fundamental component of numerous robotics applications. Prominent examples involve pose estimation, point cloud alignment, or object tracking. Algorithms for solving these estimation problems need to cope with new challenges due to an increased use of potentially poor low-cost sensors, and an ever growing deployment of robotic algorithms in consumer products which operate in potentially unknown environments. These algorithms need to be capable of being robust against strong nonlinearities, high uncertainty levels, and numerous outliers. However, particularly in robotics, the Gaussian assumption is prevalent in solutions to multivariate parameter estimation problems without providing the desired level of robustness. The goal of this tutorial is helping to address the aforementioned challenges by providing an introduction to robust estimation with a particular focus on robotics. First, this is achieved by giving a concise overview of the theory on M-estimation. M-estimators share many of the convenient properties of least-squares estimators, and at the same time are much more robust to deviations from the Gaussian model assumption. Second, we present several example applications where M-Estimation is used to increase robustness against nonlinearities and outliers.

Posted in: Probability and statistics , Tagged:

Spatio-temporal maps for mobile robots: taking into account time into the map

June 22, 2017 09:14 ,

João Machado Santos, Tomáš Krajník, Tom Duckett, Spatio-temporal exploration strategies for long-term autonomy of mobile robots, Robotics and Autonomous Systems, Volume 88, February 2017, Pages 116-126, ISSN 0921-8890, DOI: 10.1016/j.robot.2016.11.016.

We present a study of spatio-temporal environment representations and exploration strategies for long-term deployment of mobile robots in real-world, dynamic environments. We propose a new concept for life-long mobile robot spatio-temporal exploration that aims at building, updating and maintaining the environment model during the long-term deployment. The addition of the temporal dimension to the explored space makes the exploration task a never-ending data-gathering process, which we address by application of information-theoretic exploration techniques to world representations that model the uncertainty of environment states as probabilistic functions of time. We evaluate the performance of different exploration strategies and temporal models on real-world data gathered over the course of several months. The combination of dynamic environment representations with information-gain exploration principles allows to create and maintain up-to-date models of continuously changing environments, enabling efficient and self-improving long-term operation of mobile robots.

Posted in: Mobile robot mapping , Tagged: ,

Efficient detection of glass obstacles when using a laser rangefinder

June 22, 2017 09:07 ,

Xun Wang, JianGuo Wang, Detecting glass in Simultaneous Localisation and Mapping, Robotics and Autonomous Systems, Volume 88, February 2017, Pages 97-103, ISSN 0921-8890, DOI: 10.1016/j.robot.2016.11.003.

Simultaneous Localisation and Mapping (SLAM) has become one of key technologies used in advanced robot platform. The current state-of-art indoor SLAM with laser scanning rangefinders can provide accurate realtime localisation and mapping service to mobile robotic platforms such as PR2 robot. In recent years, many modern building designs feature large glass panels as one of the key interior fitting elements, e.g. large glass walls. Due to the transparent nature of glass panels, laser rangefinders are unable to produce accurate readings which causes SLAM functioning incorrectly in these environments. In this paper, we propose a simple and effective solution to identify glass panels based on the specular reflection of laser beams from the glass. Specifically, we use a simple technique to detect the reflected light intensity profile around the normal incident angle to the glass panel. Integrating this glass detection method with an existing SLAM algorithm, our SLAM system is able to detect and localise glass obstacles in realtime. Furthermore, the tests we conducted in two office buildings with a PR2 robot show the proposed method can detect ∼ 95% of all glass panels with no false positive detection. The source code of the modified SLAM with glass detection is released as a open source ROS package along with this paper.

Posted in: Robot sensors , Tagged:

Improving sensory information, diagnosis and fault tolerance by using multiple sensors and sensor fusion, with a good related work section (2.3) on fault tolerance on data fusion

June 22, 2017 09:00 ,

Kaci Bader, Benjamin Lussier, Walter Schön, A fault tolerant architecture for data fusion: A real application of Kalman filters for mobile robot localization, Robotics and Autonomous Systems, Volume 88, February 2017, Pages 11-23, ISSN 0921-8890, DOI: 10.1016/j.robot.2016.11.015.

Multisensor perception has an important role in robotics and autonomous systems, providing inputs for critical functions including obstacle detection and localization. It is starting to appear in critical applications such as drones and ADASs (Advanced Driver Assistance Systems). However, this kind of complex system is difficult to validate comprehensively. In this paper we look at multisensor perception systems in relation to an alternative dependability method, namely fault tolerance. We propose an approach for tolerating faults in multisensor data fusion that is based on the more traditional method of duplication–comparison, and that offers detection and recovery services. We detail an example implementation using Kalman filter data fusion for mobile robot localization. We demonstrate its effectiveness in this case study using real data and fault injection.

Posted in: Robot sensors , Tagged: , ,