[show abstract][hide abstract] ABSTRACT: Abstract - One-shot methods and recently proposed multi-shot methods for computing stabilizing solutions of continuoustime periodic Riccati differential equations are examined and evaluated on two test problems. The first problem arises from a stabilization problem for an artificially constructed time-varying linear systems for which the exact solution is known. The second problem originates from a nonlinear stabilization problem for numercial comparisons have been performed using both general purpose and symplectic integration methods for solving the associated Hamiltontian differential systems. In the multi-shot method a stable subspace is determined using recently published algorithms for computing a reodered periodic real Schur form. The obtained results show the increased accuracy achievable by combining multi-shot methods with structure preserving (symplectic) integration techniques.
[show abstract][hide abstract] ABSTRACT: Virtual environment-assisted teleoperation has great potential as a human-robot interaction paradigm for field robotic systems, in particular when combined with elements of automation. Unstructured outdoor environments present a complex problem with many challenging elements. For the specific application of forestry machines, we investigate which steps are required in order to implement such a system, what potential benefits there are, and how individual components can be adapted to efficiently assist forestry machine operators in their daily work in the near future. An experimental prototype of a teleoperation system with virtual environment-based feedback is constructed using a scenario-based design process. The feasibility of the implementation is partly verified through experimental studies.
Journal of Human-Robot Interaction. 01/2013; 2(3).
[show abstract][hide abstract] ABSTRACT: We consider a benchmark example of a three-link planar biped walker with torso, which is actuated in between the legs. The torso is thought to be kept upright by two identical torsional springs. The mathematical model reflects a three-degree-of-freedom mechanical system with impulse effects, which describe the impacts of the swing leg with the ground, and the aim is to induce stable limit-cycle walking on level ground. The main contribution is a novel systematic trajectory planning procedure for solving the problem of gait synthesis. The key idea is to find a system of ordinary differential equations for the functions describing a synchronization pattern for the time evolution of the generalized coordinates along a periodic motion. These functions, which are known as virtual holonomic constraints, are also used to compute an impulsive linear system that approximates the time evolution of the subset of coordinates that are transverse to the orbit of the continuous part of the periodic solution. This auxiliary system, which is known as transverse linearization, is used to design a nonlinear exponentially orbitally stabilizing feedback controller. The performance of the closed-loop system and its robustness with respect to various perturbations and uncertainties are illustrated via numerical simulations.
IEEE Transactions on Robotics 01/2013; 29(3):589-601. · 2.57 Impact Factor
[show abstract][hide abstract] ABSTRACT: This paper is based on a new procedure for dynamic output feedback design for systems with nonlinearities satisfying quadratic constraints. The new procedure is motivated by the challenges of output feedback control design for the 3-state Moore-Greitzer compressor model. First, we use conditions for stability of a transformed system and the associated matching conditions to find the data of the stabilizing controllers for the surge subsystem. Second, using the set of stabilizing controllers satisfying the given constraints for the closed-loop system with the dynamic output feedback controller we made optimization over the parameter set. We present the data of the stabilizing controllers and the new constraints for the corresponding parameters. The contributions in this paper are simplified conditions for the synthesis and optimization over the control parameter set.
[show abstract][hide abstract] ABSTRACT: The paper extends the notion of oscillations in the sense of Yakubovich to hybrid dynamics. Several sufficient stability and instability conditions for a forward invariant set are presented. The consideration is illustrated by the analysis of a model of two-link compass-gait biped robot.
Nonlinear Analysis Hybrid Systems 01/2013; · 1.69 Impact Factor
[show abstract][hide abstract] ABSTRACT: A new approach to trajectory planning for underactuated mechanical systems is presented and discussed based on analysis of feasible behaviors of a standard 2-DOF benchmark example — the cart–pendulum system. Following the Controlled Lagrangians approach of Bloch et al. (2000) , we present and re-establish known conditions and forms of feedback control laws for this example, which are leading to an equivalent completely integrable closed-loop Euler–Lagrange system; and then extend them. As shown, full integrability and, in particular, the presence of a linear in velocities first integral of dynamics plays the key role in an elegant new procedure for trajectory planning.
European Journal of Control 01/2013; 19(6):438–444. · 1.25 Impact Factor
[show abstract][hide abstract] ABSTRACT: We consider planning and implementation of fast motions for industrial manipulators constrained to a given geometric path. With such a problem formulation, which is quite reasonable for many standard operation scenarios, it is intuitively clear that a feedback controller should be designed to achieve orbital stabilization of a time-optimal trajectory instead asymptotic. We propose an algorithm to convert an asymptotically stabilizing controller into an orbitally stabilizing one and check achievable performance in simulations and, more importantly, in experiments performed on a standard industrial robot ABB IRB 140 with the IRC5-system extended with an open control interface. It is verified that the proposed re-design allows significantly reduced deviations of the actual trajectories from the desired one at high speeds not only for a chosen base feedback design but also outperforming the state-of-the-art commercial implementation offered by ABB Robotics.
Intelligent Robots and Systems (IROS), 2013 IEEE/RSJ International Conference on; 01/2013
[show abstract][hide abstract] ABSTRACT: Analysis of metabolomics data often goes beyond the task of discovering biomarkers and can be aimed at recovering other important characteristics of observed metabolomic changes. In this paper we explore different methods to detect the presence of distinctive phases in seasonal-responsive changes of metabolomic patterns of Siberian spruce (Picea obovata) during cold acclimation occurred in the period from mid-August to January. Multivariate analysis, specifically orthogonal projection to latent structures discriminant analysis (OPLS-DA), identified time points where the metabolomic patterns underwent substantial modifications as a whole, revealing four distinctive phases during acclimation. This conclusion was re-examined by a univariate analysis consisting of multiple pair-wise comparisons to identify homogeneity intervals for each metabolite. These tests complemented OPLS-DA, clarifying biological interpretation of the classification: about 60% of metabolites found responsive to the cold stress indeed changed at one or more of the time points predicted by OPLS-DA. However, the univariate approach did not support the proposed division of the acclimation period into four phases: less than 10% of metabolites altered during the acclimation had homogeneous levels predicted by OPLS-DA. This demonstrates that coupling the classification found by OPLS-DA and the analysis of dynamics of individual metabolites obtained by pair-wise multicomparisons reveals a more correct characterization of biochemical processes in freezing tolerant trees and leads to interpretations that cannot be deduced by either method alone. The combined analysis can be used in other 'omics'-studies, where response factors have a causal dependence (like the time in the present work) and pair-wise multicomparisons are not conservative. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s11306-011-0304-5) contains supplementary material, which is available to authorized users.
[show abstract][hide abstract] ABSTRACT: This paper considers switching output feedback control of linear systems and variable-structure systems. Theory for stability analysis and design for a class of observer-based feedback control systems is presented. A circle-criterion approach can be used to design an observer-based state feedback control which yields a closed-loop system with specified robustness characteristics. The approach is relevant for variable structure system design with preservation of stability when switching feedback control or sliding mode control is introduced in the feedback loop. It is shown that there exists a Lyapunov function valid over the total operating range and this Lyapunov function has also interpretation as a storage function of passivity-based control. The Lyapunov function can be found by solving a Lyapunov equation, which also generates variable structure switching surfaces. Important applications are to be found in variable structure systems with high robustness requirements.
[show abstract][hide abstract] ABSTRACT: Successful recognition and pose estimation of logs and trees as well as workspace modeling in the forest environment is essential for extensive automation of the harvesting and logging tasks of forestry machines. However, the free form features of logs, few reliable textural features, large edge extraction errors, and segmentation faults caused by the barks on the surface of the logs present clear challenges for recognition and classification. To solve these problems, robust algorithms able to recognize and estimate poses of a variety of objects even under poor and partial inputs need to be developed. In this paper we focus on the most relevant task of recognizing and estimating postures of a bunch of logs located on the ground with varying orientation and distance. Experiments carried out with the help of a structured light camera demonstrate the feasibility of the proposed algorithm.
Robotics and Automation (ICRA), 2011 IEEE International Conference on; 06/2011
[show abstract][hide abstract] ABSTRACT: A short term goal in the forest industry is semi-automation of existing machines for the tasks of logging and harvesting. One way to assist drivers is to provide a set of predefined trajectories that can be used repeatedly in the process. In recent years much effort has been directed to the design of control strategies and task planning as part of this solution. However, commercialization of such automatic schemes requires the installation of various sensing devices, computers and most of all a redesign of the machine itself, which is currently undesired by manufacturers. Here we present an approach of implementing predefined trajectories in an open-loop fashion, which avoids the complexity of sensor and computer integration. The experimental results are carried out on a commercial hydraulic crane to demonstrate that this solution is feasible in practice.
IEEE International Conference on Robotics and Automation, ICRA 2011, Shanghai, China, 9-13 May 2011; 01/2011
[show abstract][hide abstract] ABSTRACT: We consider a 24-degrees-of-freedom monkey robot that is supposed to perform brachiation locomotion, i.e. swinging from one row of a horizontal ladder to the next one using the arms. The robot hand is constructed as a planar hook so that the contact point about which the robot swings is a passive hinge. We identify the 10 most relevant degrees of freedom for this underactuated mechanical system and formulate a tractable search: (a) introduce a family of coordination patterns to be enforced on the dynamics with respect to a path coordinate; (b) formulate geometric equality constraints that are necessary for periodic locomotion; (c) generate trajectories from integrable reduced dynamics associated with the passive hinge; (d) evaluate the energetic cost of transport. Moreover, we observe that a linear approximation of the reduced dynamics can be used for trajectory generation which allows us to incorporate the gradient of the cost function into the search algorithm.
2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, IROS 2011, San Francisco, CA, USA, September 25-30, 2011; 01/2011
[show abstract][hide abstract] ABSTRACT: Nonlinear H-infinity synthesis is developed to solve the tracking control problem into a 3-DOF helicopter prototype. Planning of periodic motions under a virtual constraints approach is considered prior the controller design in order to achieve our goal. A local H-infinity controller is derived by means of a certain perturbation of the differential Riccati equations that appear while solving the corresponding H-infinity control problem for the linearised system. Stabilisability and detectability properties of the control system are thus ensured by the existence of the proper solutions of the unperturbed differential Riccati equations, and hence the proposed synthesis procedure obviates an extra verification work of these properties. Due to the nature of the approach, the resulting controller additionally yields the desired robustness properties against unknown but bounded external disturbances. Convergence and robustness of the proposed design are supported by simulation results.
International Journal of Systems Science 01/2011; 42(5):829-838. · 1.31 Impact Factor
[show abstract][hide abstract] ABSTRACT: Ball dribbling is a central element of basketball. One main challenge for realizing basketball robots is to stabilize periodic motion of the ball. The task is nontrivial due to the discrete-continuous nature of the corresponding dynamics. This paper proposes to add an elastic element to the manipulator so the ball can be controlled in a continuous-time phase instead of an intermittent contact. Optimal catching and pushing trajectories are planned for the underactuated system based on the virtual holonomic constraints approach. First experimental studies are presented to evaluate the approach.
Intelligent Robots and Systems (IROS), 2010 IEEE/RSJ International Conference on; 11/2010
[show abstract][hide abstract] ABSTRACT: We consider trajectory planning for an underactuated 3DOF helicopter, using the virtual holonomic constraint approach. First we choose constraint functions that describe the configuration variables along a desired motion in terms of some independent parametrization variable. This lets us describe the closed-loop system by some reduced order dynamics, the solution of which gives a feasible trajectory for the desired motion. By using the method of transverse linearization for controller design, we achieve exponential orbital stability to a desired trajectory. Numerical simulations confirm this property and show good convergence to a desired periodic motion when initialized from a resting state.
Intelligent Robots and Systems (IROS), 2010 IEEE/RSJ International Conference on; 11/2010
[show abstract][hide abstract] ABSTRACT: A new approach for solving an optimal control problem of ball pitching with an underactuated human-like robot arm is proposed. The system dynamics is simplified to a planar two-link robot with actuation only at the shoulder joint and a passive spring at the elbow joint representing the stiffness of the arm. The objective is to accelerate the ball from an initial configuration at rest in such a way that the projection of its velocity along a certain elevation angle is maximal at a predefined release line. The suggested procedure makes use of a parameterization of the robot motion in terms of geometric relations among the generalized coordinates. We systematically formulate a necessary condition for an optimal motion resulting in a nonlinear differential equation that describes a synchronization of the joint angles. A suitable solution is found by numerically searching over a finite number of free initial conditions.
Robotics and Automation (ICRA), 2010 IEEE International Conference on; 06/2010
[show abstract][hide abstract] ABSTRACT: Ball dribbling is a central element of basketball. One main challenge for realizing basketball robots is to stabilize periodic motions of the ball. This task is nontrivial due to the discrete-continuous nature of the corresponding dynamics. The ball can be only controlled during ball-manipulator contact and moves freely otherwise. We propose a manipulator equipped with a spring that gets compressed when the ball bounces against it. Hence, we can have continuous-time control over this underactuated Ball-Spring-Manipulator system until the spring releases its accumulated energy back to the ball. This paper illustrates a systematic way of planning such a modified dribbling motion, computing an analytical transverse linearization and achieving orbital stabilization.
Robotics and Automation (ICRA), 2010 IEEE International Conference on; 06/2010
[show abstract][hide abstract] ABSTRACT: This study examines the mechanical systems with an arbitrary number of passive (non-actuated) degrees of freedom and proposes an analytical method for computing coefficients of a linear controlled system, solutions of which approximate dynamics transverse to a feasible motion. This constructive procedure is based on a particular choice of coordinates and allows explicit introduction of a moving Poincare?? section associated with a nontrivial finite-time or periodic motion. In these coordinates, transverse dynamics admits analytical linearization before any control design. If the forced motion of an underactuated mechanical system is periodic, then this linearization is an indispensable and constructive tool for stabilizing the cycle and for analyzing its orbital (in)stability. The technique is illustrated with two challenging examples. The first one is stabilization of a circular motions of a spherical pendulum on a puck around its upright equilibrium. The other one is creating stable synchronous oscillations of an arbitrary number of planar pendula on carts around their unstable equilibria.
IEEE Transactions on Automatic Control 05/2010; · 2.72 Impact Factor
[show abstract][hide abstract] ABSTRACT: Efficient and accurate structure exploiting numerical methods for solving the periodic Riccati differential equation (PRDE)
are addressed. Such methods are essential, for example, to design periodic feedback controllers for periodic control systems.
Three recently proposed methods for solving the PRDE are presented and evaluated on challenging periodic linear artificial
systems with known solutions and applied to the stabilization of periodic motions of mechanical systems. The first two methods
are of the type multiple shooting and rely on computing the stable invariant subspace of an associated Hamiltonian system.
The stable subspace is determined using either algorithms for computing an ordered periodic real Schur form of a cyclic matrix
sequence, or a recently proposed method which implicitly constructs a stable deflating subspace from an associated lifted
pencil. The third method reformulates the PRDE as a convex optimization problem where the stabilizing solution is approximated
by its truncated Fourier series. As known, this reformulation leads to a semidefinite programming problem with linear matrix
inequality constraints admitting an effective numerical realization. The numerical evaluation of the PRDE methods, with focus
on the number of states (n) and the length of the period (T) of the periodic systems considered, includes both quantitative and qualitative results.
KeywordsPeriodic systems-Periodic Riccati differential equations-Orbital stabilization-Periodic real Schur form-Periodic eigenvalue reordering-Hamiltonian systems-Linear matrix inequalities-Numerical methods
Mathematics Subject Classification (2000)15A21-15A39-34K13-49N05-65F15-65P10-70M20-70Q05-90C22