Loosely interconnected cooperative systems such as cable robots are particularly susceptible to uncertainty. Such uncertainty is exacerbated by addition of the base mobility to realize reconfigurability within the system. However, it also sets the ground for predictive base reconfiguration in order to reduce the uncertainty level in system response. To this end, in this paper, we systematically quantify the output wrench uncertainty based on which a base reconfiguration scheme is proposed to reduce the uncertainty level for a given task (uncertainty manipulation). Variations in the tension and orientation of the cables are considered as the primary sources of the uncertainty responsible for nondeterministic wrench output on the platform. For nonoptimal designs/configurations, this may require complex control structures or lead to system instability. The force vector corresponding to each agent (e.g., pulley and cable) is modeled as random vector whose magnitude and orientation are modeled as random variables with Gaussian and von Mises distributions, respectively. In a probabilistic framework, we develop the closed-form expressions of the means and variances of the output force and moment given the current state (tension and orientation of the cables) of the system. This is intended to enable the designer to efficiently characterize an optimal configuration (location) of the bases in order to reduce the overall wrench fluctuations for a specific task. Numerical simulations as well as real experiments with multiple iRobots are performed to demonstrate the effectiveness of the proposed approach.
Traditional kinematic analysis of manipulators, built upon a deterministic articulated kinematic modeling often proves inadequate to capture uncertainties affecting the performance of the real robotic systems. While a probabilistic framework is necessary to characterize the system response variability, the random variable/vector based approaches are unable to effectively and efficiently characterize the system response uncertainties. Hence in this paper, we propose a random matrix formulation for the Jacobian matrix of a robotic system. It facilitates characterization of the uncertainty model using limited system information in addition to taking into account the structural inter-dependencies and kinematic complexity of the manipulator. The random Jacobian matrix is modeled such that it adopts a symmetric positive definite random perturbation matrix. The maximum entropy principle permits characterization of this perturbation matrix in the form of a Wishart distribution with specific parameters. Comparing to the random variable/vector based schemes, the benefits now include: incorporating the kinematic configuration and complexity in the probabilistic formulation, achieving the uncertainty model using limited system information (mean and dispersion parameter), and realizing a faster simulation process. A case study of a 6R serial manipulator (PUMA 560) is presented to highlight the critical aspects of the process. A Monte Carlo analysis is performed to capture the deviations of distal path from the desired trajectory and the statistical analysis on the realizations of the end effector position and orientation shows how the uncertainty propagates throughout the system.
In this paper, we generalize our random matrix based (RM-based) uncertainty model for manipulator Jacobian matrix to the dynamic model of the robotic systems. Conventional random variable based (RV-based) schemes require a detailed knowledge of the system parameters variation and may be not able to fully characterize the uncertainties of the complex dynamic systems. However, the proposed RM-based approach provides a probabilistic framework for systematic characterization of the uncertainties in the complex systems with limited available information. Moreover, RM-based uncertainty model is an efficient mathematical tool that ensures the kinematic and dynamic consistency and takes into account the system complexity, configuration, structural inter-dependencies, etc. The application of the RM-based uncertainty model is investigated using an example of kinematically redundant planar parallel manipulator (3-(P)RRR). The simulation results are compared with those obtained through conventional RV-based approach and the effectiveness of the proposed method is discussed.
In this paper, we formulate the manipulator Jacobian matrix in a probabilistic framework based on the random matrix theory (RMT). Due to the limited available information on the system fluctuations, the parametric approaches often prove to be inadequate to appro-priately characterize the uncertainty. To overcome this difficulty, we develop two RMT-based probabilistic models for the Jacobian matrix to provide systematic frameworks that facilitate the uncertainty quantification in a variety of complex robotic systems. One of the models is built upon direct implementation of the maximum entropy principle that results in a Wishart random perturbation matrix. In the other probabilistic model, the Ja-cobian matrix is assumed to have a matrix-variate Gaussian distribution with known mean. The covariance matrix of the Gaussian distribution is obtained at every time point by maximizing a Shannon entropy measure (subject to Jacobian norm and covariance positive semidefiniteness constraints). In contrast to random variable/vector based schemes, the benefits of the proposed approach now include: (i) incorporating the kine-matic configuration and complexity in the probabilistic formulation; (ii) achieving the uncertainty model using limited available information; (iii) taking into account the work-ing configuration of the robotic systems in characterization of the uncertainty; and (iv) realizing a faster simulation process. A case study of a 2R serial manipulator is presented to highlight the critical aspects of the process. [DOI: 10.1115/1.4027871]
In this paper, we address the enhanced state estimation and prediction system for automobile applications by fusing relatively low-cost and noisy Inertial Navigation System (INS) sensing with Global Positioning System (GPS) measurements. An unscented Kalman filter is used to merge multi-rate measurements from GPS and INS sensors together with a high-fidelity vehicle-dynamics model for state-predictions. The high-fidelity motion model (including suspension-effects) for the vehicle motion trajectory on uneven terrain is captured by a 20-state system of nonlinear differential equations. Computer simulation results illustrate the effectiveness of sensor-fusion (building upon the merger of an inexpensive INS sensing with GPS based measurements) to accurately estimate the full system-state. The relative ease of implementation, accuracy and predictive performance with low-cost sensing will facilitate its use in various electronic control and safety-systems, such as Electronic Stability Program, Anti-lock Brake Systems, and the Lateral Dynamic Stability Control.
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