Friday, June 22. 2012
Carla M.A. Pinto2 *,Cristina P. Santos**, Diana Rocha*, Vitor Matos** * Instituto Superior de Engenharia do Porto and Centro de Matematica da Universidade do Porto Rua Dr Antonio Bernardino de Almeida, 431, 4200-072 Porto, Portugal ** Dept. Electronica Industrial and Centro Algoritmi Universidade do Minho Campus de Azurem 4800-058 Guimaraes, Portugal Received 30 January, 2011; accepted in revised form 19 June, 2012 Abstract: There has been considerable development in the design of efficient controllers for trajectory follow- ing in articulated robots with many degrees-of-freedom. Nevertheless generating trajectories online is still a complex and unsatisfactorily solved problem. In this paper we present a new architecture for a Central Pattern Generator (CPG), for online generation of trajectories in quadruped robots. Our model is based on a CPG model for locomotor rhythms of quadruped animals, proposed by Golubitsky, Stewart, Buono, and Collins. Their model consists of eight coupled cells (CPG units) and each CPG unit is modeled as an oscillator by a system of ordinary differential equations (ODEs). We generalize their CPG model, considering that each cell or CPG unit is divided in rhythmic and discrete motor primitives, modeled by simple nonlinear systems of ODEs. Superposition of discrete and rhythmic primitives may allow for more complex motor behaviours, namely locomotion in irregular terrain and obstacle avoidance. In this paper, the discrete primitive is inserted into the rhythmic one (i) as an offset of the solution, (ii) summed to the solution of the rhythmic primitive. We also consider three types of couplings between CPG units: synaptic, diffusive and mixed. In this article we try to tackle the impact that these discrete corrections may have in the achieved system solu- tions. Numerical results show that amplitude and frequency of the periodic solutions are almost constant for all couplings in cases (i) and (ii). The larger variation occurs in the values of amplitude and frequency for case (i) in the synaptic coupling. Results are also obtained in a robotic experiment using a simulated AIBO robot that walks over a ramp. Am- plitude and frequency may be identified, respectively, with the range of motion and the velocity of the robots’ movement.
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Friday, June 22. 2012
Carla M.A. Pinto2 *, Diana Rocha*, Cristina P. Santos** * Instituto Superior de Engenharia do Porto and Centro de Matematica da Universidade do Porto Rua Dr Antonio Bernardino de Almeida, 431, 4200-072 Porto, Portugal ** Universidade do Minho Dept. Electronica Industrial Campus de Azurem 4800-058 Guimaraes, Portugal Received 29 December, 2011; accepted in revised form 19 June, 2012 Abstract: Humanoid robots have been extensively studied in the last few years. The motivation for this study is that bipedal locomotion is superior to wheeled approaches on real terrain and situations where robots accompany or replace humans. Some examples are, on the development of human assisting device, such as prosthetics, orthotics, and devices for rehabilitation, rescue of wounded troops, maidens, accompany and assistance to elderly people, amongst others. Online generation of trajectories for these robots is a complex process, that includes different types of movements, i.e., distinct motor primitives. In this paper, we consider two motor primitives: rhythmic and discrete. We study the effect on a bipeds robots’ gaits of inserting the discrete part as an offset of the rhythmic primitive, for synaptic and diffusive couplings. We also study stability of biped gaits. We simulate a periodic solution corresponding to the biped run, for the variation of the discrete offset. We find that amplitude and frequency of this periodic solution, are almost constant in all cases studied. This is useful when considering implementations of the proposed controllers for generating trajectories for the joints of real biped robots.
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Friday, June 22. 2012
Carla M.A. Pinto*, Diana Rocha*, Cristina P. Santos** * Instituto Superior de Engenharia do Porto and Centro de Matematica da Universidade do Porto Rua Dr Antonio Bernardino de Almeida, 431, 4200-072 Porto, Portugal ** Universidade do Minho Dept. Electronica Industrial Campus de Azurem 4800-058 Guimaraes, Portugal Received 9 December, 2011; accepted in revised form 19 June, 2012 Abstract: Legged robots are often used in a large variety of tasks, in different environments. The large number of degrees-of-freedom, to be controlled during these tasks, turns the online generation of trajectories in these robots very complex. In this paper, we consider a modular approach to online generation of trajectories, based on biological concepts, namely Central Pattern Generators (CPGs). We introduce a new CPG model for hexapod robots’ rhythms, that generalizes the work of Golu- bitsky, Stewart, Buono and Collins (1998,1999). Each neuron/oscillator in the CPG consists of two modules/primitives: rhythmic and discrete, that are modeled by nonlinear dynamical systems. Su- perposition of discrete and rhythmic primitives permits the modeling of complex motor behaviors, namely locomotion in irregular terrain and obstacle avoidance. We study the effect on the amplitude and frequency of the robots’ gaits of superimposing the two motor primitives. The discrete primi- tive is inserted as an offset of the solution of the rhythmic primitive. We also consider three types of couplings between CPG units: synaptic, diffusive and mixed. Simulation results reveal interesting facts, in certain cases amplitude and frequency of periodic solutions, identified with hexapods’ tripod, caterpillar and metachronal gaits, remain constant. Therefore, it is possible to use these solutions to generate trajectories for the joint values of real six-legged robots, since varying the joint offset will not affect the required amplitude and frequency of the resultant trajectory nor the gait.
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Friday, June 22. 2012
O. Koch Institute for Analysis and Scientific Computing (E101), Vienna University of Technology, Wiedner Hauptstrasse 8–10, A-1040 Wien, Austria Received 6 February, 2009; accepted in revised form 20 December, 2011 Abstract: We discuss the numerical approximation of the solution to the multi- configuration time-dependent Hartree-Fock (MCTDHF) equations in quantum dynamics. The associated equations of motion, obtained via the Dirac–Frenkel time-dependent varia- tional principle, consist of a coupled system of low-dimensional nonlinear partial differential equations and ordinary differential equations. We extend the analysis of the convergence of a time integrator based on splitting of the vector field for systems of unbound fermions to the case where a nuclear attractive potential is present. First order convergence in the H 1 norm and second order convergence in L2 are established. The analysis applies to electronic states whose density vanishes at the nucleus.
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