Solution intervals for variables in spatial RCRCR linkages

© 2019. ElsevierAn analytic method to compute the solution intervals for the input variables of spatial RCRCR linkages and their inversions is presented. The input-output equation is formulated as the intersection of a single ellipse with a parameterized family of ellipses, both related with the possible values that certain dual angles determined by the configuration of the mechanism can take. Bounds for the angles of the input pairs of the RCRCR and RRCRC inversions are found by imposing the tangency of two ellipses, what reduces to analyzing the discriminant of a fourth degree polynomial. The bounds for the input pair of the RCRRC inversion is found as the intersection of a single ellipse with the envelope of the parameterized family of ellipses. The method provides the bounds of each of the assembly modes of the mechanism as well as the local extrema that may exist for the input variablePeer ReviewedPostprint (author's final draft

Competitive function approximation for reinforcement learning

The application of reinforcement learning to problems with continuous domains requires representing the value function by means of function approximation. We identify two aspects of reinforcement learning that make the function approximation process hard: non-stationarity of the target function and biased sampling. Non-stationarity is the result of the bootstrapping nature of dynamic programming where the value function is estimated using its current approximation. Biased sampling occurs when some regions of the state space are visited too often, causing a reiterated updating with similar values which fade out the occasional updates of infrequently sampled regions. We propose a competitive approach for function approximation where many different local approximators are available at a given input and the one with expectedly best approximation is selected by means of a relevance function. The local nature of the approximators allows their fast adaptation to non-stationary changes and mitigates the biased sampling problem. The coexistence of multiple approximators updated and tried in parallel permits obtaining a good estimation much faster than would be possible with a single approximator. Experiments in different benchmark problems show that the competitive strategy provides a faster and more stable learning than non-competitive approaches.Preprin

Second order collocation

Technical reportCollocation methods for optimal control commonly assume that the system dynamics is expressed as a first order ODE of the form dx/dt = f(x, u, t), where x is the state and u the control vector. However, in many cases, the dynamics involve the second order derivatives of the coordinates: d^2q/t^2 = g(q, dq/dt, u, t), so that, to preserve the first order form, the usual procedure is to introduce one velocity variable for each coordinate and define the state as x = [q,v]T, where q and v are treated as independent variables. As a consequence, the resulting trajectories do not fulfill the mandatory relationship v = dq/dt except at the collocation points, where it is explicitly imposed. We propose a formulation for Trapezoidal and Hermite-Simpson collocation methods adapted to deal directly with second order dynamics without the need to introduce v as independent from q, and granting the consistency of the trajectories for q and v.Preprin

A competitive strategy for function approximation in Q-learning

In this work we propose an approach for generalization in continuous domain Reinforcement Learning that, instead of using a single function approximator, tries many different function approximators in parallel, each one defined in a different region of the domain. Associated with each approximator is a relevance function that locally quantifies the quality of its approximation, so that, at each input point, the approximator with highest relevance can be selected. The relevance function is defined using parametric estimations of the variance of the q-values and the density of samples in the input space, which are used to quantify the accuracy and the confidence in the approximation, respectively. These parametric estimations are obtained from a probability density distribution represented as a Gaussian Mixture Model embedded in the input-output space of each approximator. In our experiments, the proposed approach required a lesser number of experiences for learning and produced more stable convergence profiles than when using a single function approximator.Peer ReviewedPreprin

Exact interval propagation for the efficient solution of position analysis problems on planar linkages

This paper presents an interval propagation algorithm for variables in planar single-loop linkages. Given intervals of allowed values for all variables, the algorithm provides, for every variable, the whole set of values, with out over-estimation, for which the linkage can actually be assembled. We show further how this algorithm can be integrated in a branch-and-prune search scheme, in order to solve the position analysis of general planar multi-loop linkages. Experimental results are included, comparing the method’s perfor mance with that of previous techniques given for the same task.Peer ReviewedPostprint (author's final draft

Stochastic approximations of average values using proportions of samples

IRI Technical ReportIn this work we explain how the stochastic approximation of the average of a random variable is carried out when the observations used in the updates consist in proportion of samples rather than complete samples.Preprin

Exact interval propagation for the efficient solution of planar linkages

This paper presents an interval propagation algorithm for variables in single-loop linkages. Given allowed intervals of values for all variables, the algorithm provides, for every variable, the exact interval of values for which the linkage can actually be assembled. We show further how this algorithm can be integrated in a branch-and bound search scheme, in order to solve the position analysis of general multi-loop linkages. Experimental results are included, comparing the method’s performance with that of previous techniques given for the same task.Peer Reviewe

Description of a robotics-oriented relational positioning methodology

This paper presents a relational positioning methodology for flexibly and intuitively specifying offline programmed robot tasks, as well as for assisting the execution of teleoperated tasks demanding precise movements. In relational positioning, the movements of an object can be restricted totally or partially by specifying its allowed positions in terms of a set of geometric constraints. These allowed positions are found by means of a 3D sequential geometric constraint solver called PMF – Positioning Mobile with respect to Fixed. PMF exploits the fact that in a set of geometric constraints, the rotational component can often be separated from the translational one and solved independently

Robot task specification and execution through relational positioning

This paper presents a relational positioning methodology for flexibly and intuitively specifying offline programmed robot tasks, and for assisting the execution of teleoperated tasks featuring precise or repetitive movements. By formulating an object positioning problem in terms of symbolic geometric constraints, the movements of an object can be restricted totally or partially, independently of its initial configuration. To solve the problem, a 3D sequential geometric constraint solver called PMF –Positioning Mobile with respect to Fixed– has been developed. PMF exploits the fact that in geometric constraint sets the rotational component can often be decoupled from the translational one and solved independently.Peer Reviewe

Collocation methods for second and higher order systems

It is often unnoticed that the predominant way to use collocation methods is fundamentally flawed when applied to optimal control in robotics. Such methods assume that the system dynamics is given by a first order ODE, whereas robots are often governed by a second or higher order ODE involving configuration variables and their time derivatives. To apply a collocation method, therefore, the usual practice is to resort to the well known procedure of casting an Mth order ODE into M first order ones. This manipulation, which in the continuous domain is perfectly valid, leads to inconsistencies when the problem is discretized. Since the configuration variables and their time derivatives are approximated with polynomials of the same degree, their differential dependencies cannot be fulfilled, and the actual dynamics is not satisfied, not even at the collocation points. This paper draws attention to this problem, and develops improved versions of the trapezoidal and Hermite-Simpson collocation methods that do not present these inconsistencies. In many cases, the new methods reduce the dynamic transcription error in one order of magnitude, or even more, without noticeably increasing the cost of computing the solutions.Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This work has been partially funded by Agencia Estatal de Investigación under project Kinodyn+, with reference PID2020-117509GB-I00/AEI /10.13039/50110001103, and by a Ph.D. contract supporting the first author, with reference PRE2018-085582.Peer ReviewedPostprint (published version