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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.
Robotics and Automation (ICRA), 2011 IEEE International Conference on; 06/2011
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ABSTRACT: In the forest industry, trees are logged and harvested by human-operated hydraulic manipulators. Eventually, these tasks are expected to be automated with optimal performance. However, with todays technology the main problem is implementation. While prototypes may have rich sensing information, real cranes lack certain sensing devices, such as encoders for position sensing. Automating these machines requires unconventional solutions. In this paper, we consider the motion planning problem, which involves a redesign of optimal trajectories, so that open loop control strategies can be applied using feed-forward control signals whenever sensing information is not available.
Intelligent Robots and Systems (IROS), 2010 IEEE/RSJ International Conference on; 11/2010
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ABSTRACT: We consider a 3-link planar walker with two legs and an upper body. An actuator is introduced between the legs, and the torso is kept upright by torsional springs. The model is a 3-DOF impulsive mechanical system, and the aim is to induce stable limit-cycle walking in level ground. To solve the problem, the ideas of the virtual holonomic constraints approach are explored, used and extended. The contribution is a novel systematic motion planning procedure for solving the problem of gait synthesis, which is challenging for non-feedback linearizable mechanical systems with two or more passive degrees of freedom. For a preplanned gait we compute an impulsive linear system that approximates dynamics transversal to the periodic solution. This linear system is used for the design of a stabilizing feedback controller. Results of numerical simulations are presented to illustrate the performance of the closed loop system.
Robotics and Automation (ICRA), 2010 IEEE International Conference on; 06/2010
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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
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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; · 2.11 Impact Factor
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ABSTRACT: We consider a class of mechanical systems with an arbitrary number of passive (non-actuated) degrees of freedom. In addition to control forces, we take into account viscous and Coulomb friction forces and impacts with the environment modeled as impulsive updates of the states. We assume that a motion planning task is solved and a feasible forced periodic motion is described in terms of piece-wise smooth virtual holonomic constraints. The main contribution is an analytical method for computing coefficients of an impulsive linear control system, solutions of which approximate dynamics transversal to the preplanned trajectory. This linear system is shown to be useful for stability analysis and for design of feedback controllers orbitally stabilizing forced periodic motions in the hybrid mechanical system. As an illustration, we apply the obtained theoretical results providing a rigorous proof of orbital exponential stability of the periodic tumbling motion for a model of a descending strip of paper in a still air.
Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on; 01/2010
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IFAC Symposium on Nonlinear Control Systems; 01/2010
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NOLCOS'10; 01/2010
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ABSTRACT: A general method for planning and orbitally stabilizing periodic motions for impulsive mechanical systems with underactuation one is proposed. For each such trajectory, we suggest a constructive procedure for defining a sufficient number of nontrivial quantities that vanish on the orbit. After that, we prove that these quantities constitute a possible set of transverse coordinates. Finally, we present analytical steps for computing linearization of dynamics of these coordinates along the motion. As a result, for each such planned periodic trajectory, a hybrid transverse linearization for dynamics of the system is computed in closed form. The derived impulsive linear system can be used for stability analysis and for design of exponentially orbitally stabilizing feedback controllers. A geometrical interpretation of the method is given in terms of a novel concept of a moving Poincare section. The technique is illustrated on a devil stick example.
IEEE Transactions on Automatic Control 01/2010; · 2.11 Impact Factor
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ABSTRACT: A planar compass-like biped on a shallow slope is one of the simplest models of a passive walker. It is a 2-degree-of-freedom (DOF) impulsive mechanical system that is known to possess periodic solutions reminiscent of human walking. Finding such solutions is a challenging computational task that has attracted many researchers who are motivated by various aspects of passive and active dynamic walking. We propose a new approach to find stable as well as unstable hybrid limit cycles without integrating the full set of differential equations and, at the same time, without approximating the dynamics. The procedure exploits a time-independent representation of a possible periodic solution via a virtual holonomic constraint. The description of the limit cycle obtained in this way is useful for the analysis and characterization of passive gaits as well as for design of regulators to achieve gaits with the smallest required control efforts. Some insights into the notion of hybrid zero dynamics, which are related to such a description, are presented as well.
IEEE Transactions on Robotics 11/2009; · 2.54 Impact Factor
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ABSTRACT: The well-known and commonly accepted finite dimensional model qualitatively describing surge instabilities in centrifugal (and axial) compressors is considered. The problem of global output feedback stabilization for it is solved. The solution relies on two new criteria for global stability proposed for a class of nonlinear systems exploiting quadratic constraints for infinite sector nonlinearities. The constructive steps in developing a family of output feedback controllers based on these stability tests are presented. Performance of the closed-loop systems are illustrated by simulations.
Control Applications, (CCA) & Intelligent Control, (ISIC), 2009 IEEE; 08/2009
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ABSTRACT: In this paper we consider the motion planning and control problem of an underactuated 3DOF rigid body. The dynamics of a particular experimental setup as abstraction of the rotational degrees of freedom of a helicopter is studied. The virtual holonomic constraints approach serves as analytical tool to plan various periodic motions of the system, where a synchronization pattern among the generalized coordinates can be specified and a trajectory is obtained from reduced order dynamics. The controller design is based on a transverse linearization along a desired trajectory and ensures exponential orbital stability. Convergence to a desired motion is confirmed via numerical simulations.
Advanced Robotics, 2009. ICAR 2009. International Conference on; 07/2009
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ABSTRACT: In this paper we consider the problem of motion planning and control of a kinematically redundant manipulator, which is used on forestry machines for logging. Once a desired path is specified in the 3D world frame, a trajectory can be planned and executed such that all joints are synchronized and constrained to the Cartesian path.We introduce an optimization procedure that takes advantage of the kinematic redundancy so that time-efficient joint and velocity profiles along the path can be obtained. Differential constraints imposed by the manipulator dynamics are accounted for by employing a phase-plane technique for admissible path timings. In hydraulic manipulators, such as considered here, the velocity constraints of the individual joints are particularly restrictive. We suggest a time-independent control scheme for the planned trajectory which is built upon the standard reference tracking controllers. Experimental tests underline the benefits and efficiency of the model-based trajectory planning and show success of the proposed control strategy.
Advanced Robotics, 2009. ICAR 2009. International Conference on; 07/2009
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ABSTRACT: A class of mechanical systems with many unactuated degrees of freedom is studied. An analytical method for computing coefficients of a linear controlled system, solutions of which approximate dynamics of transverse part of coordinates of an underactuated mechanical system along a feasible motion, is proposed. The procedure is constructive and is based on a particular choice of coordinates in a vicinity of the motion. It allows explicit introduction of the so-called moving Poincare section associated with a finite-time or periodic motion. It is shown that the coordinates admit analytical linearization of transverse part of the system dynamics prior to any controller design. If the motion is periodic, then these coordinates are used for developing feedback controllers. Necessary and sufficient conditions for exponential orbital stabilization of a cycle for underactuated mechanical systems are derived. Two illustrative examples are elaborated in details.
American Control Conference, 2009. ACC '09.; 07/2009
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ABSTRACT: The problem of swinging up inverted pendulums has often been solved by stabilization of a particular class of homoclinic structures present in the dynamics of the standard pendulum. In this article new arguments are suggested to show how different homoclinic curves can be preplanned for dynamics of the passive-link of the robot. This is done by reparameterizing the motion according to geometrical relations among the generalized coordinates. It is also shown that under certain conditions there exist periodic solutions surrounding such homoclinic orbits. These trajectories admit designing feedback controllers to ensure exponential orbital stabilization. The method is illustrated by simulations and supported by experimental studies.
Robotics and Automation, 2009. ICRA '09. IEEE International Conference on; 06/2009
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ABSTRACT: In the field of robotics the energy spent for actuation is always an issue. It is often the case that some desired motions cannot be achieved by the robot due to limitations in actuation power. We suggest a simple solution to the problem: complement the actuators by some configuration of mechanical springs which delivers a torque profile that is well-tuned for the desired robot motion. As a result, the control effort for the original actuator will be reduced. In this case study we consider an underactuated planar two-link robot for experimental demonstration of the concept. The virtual holonomic constraints approach serves as analytical tool to parameterize, plan, and stabilize desired periodic motions.
Decision and Control, 2008. CDC 2008. 47th IEEE Conference on; 01/2009
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ABSTRACT: This paper introduces a method for analytical planning of feasible hybrid periodic trajectories in nonfeedback-linearizable impulsive mechanical systems with control inputs. For a planned motion, a procedure for computation of a transverse linearization for a class of hybrid controlled mechanical systems with underactuation one is presented. The resulting linear comparison system can be used for stability analysis and for design of orbitally stabilizing controllers.
Decision and Control, 2008. CDC 2008. 47th IEEE Conference on; 01/2009
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ABSTRACT: A planar compass-like biped on a shallow slope is the simplest model of a passive walker. It is a two-degrees-of-freedom impulsive mechanical system known to possess periodic solutions reminiscent to human walking. Finding such solutions is a challenging task. We propose a new approach to obtain stable as well as unstable hybrid limit cycles without integrating the full set of differential equations. The procedure is based on exploring the idea of parameterizing a possible periodic solution via virtual holonomic constraints. We also show that a 2-dimensional manifold, defining the hybrid zero dynamics associated with a stable hybrid cycle, in general, is not invariant for the dynamics of the model of the compass-gait walker.
Decision and Control, 2008. CDC 2008. 47th IEEE Conference on; 01/2009
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ABSTRACT: We consider the challenging problem of creating oscillations in underactuated mechanical systems. Target oscillatory motions of the indirectly actuated degree of freedom of a mechanical system can often be achieved via a straightforward to design feedback transformation. Moreover, the corresponding part of the dynamics can be forced to match a desired second-order system possessing the target periodic solution (Aracil, J., Gordillo, F., and Acosta, J.A. (2002), `Stabilization of Oscillations in the Inverted Pendulum', in Proceedings of the 15th IFAC World Congress, Barcelona, Spain; Canudas-de-Wit, C., Espiau, B., and Urrea, C. (2002), `Orbital Stabilisation of Underactuated Mechanical Systems', in Proceedings of the 15th IFAC World Congress, Barcelona, Spain). Sometimes, it is possible to establish the presence of periodic or bounded motions for the remaining degrees of freedom in the transformed system. However, typically this motion planning procedure leads to an open-loop unstable orbit and by necessity should be followed by a feedback control design. We propose a new approach for synthesis of a (practically) stabilising feedback controller, which ensures convergence of the solutions of the closed-loop system into a narrow tube around the preplanned orbit. The method is illustrated in detail by shaping oscillations in the inverted pendulum on a cart around its upright equilibrium. The complete analysis is based on application of a non-standard higher-order averaging technique assuming sufficiently high frequency of oscillations and is presented for this particular example.
International Journal of Control 01/2009; 82(9):1582-1590. · 0.98 Impact Factor
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IEEE T. Automat. Contr. 01/2009;
