Uncertainty characterization in serial and parallel manipulators using random matrix theory

ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering

Rai

Krovi

2017

Self Cite

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.

Section: Wrench Uncertaintymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Wrench Uncertainty Quantification and Reconfiguration Analysis in Loosely Interconnected Cooperative Systems

ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering

Rai

Krovi

2017

Self Cite

“…In this section, our random matrix formulation of the manipulator Jacobian matrix developed in [4], [5] is generalized to dynamic EOM of the robotic systems. The EOM of the deterministic mean dynamic system can be expressed as:…”

Section: Random Matrix Formulationmentioning

confidence: 99%

“…• Computational efficiency. In this paper, we generalize our RM-based uncertainty model for manipulator Jacobian matrix, developed in [4], [5], that is based on the non-parametric probabilistic model proposed by Soize [6], [7], to dynamic equations of motion (EOM) of the robotic systems. This provides a systematic approach that adequately satisfies the requirements noted above and can be beneficial in the design procedure of the complex dynamic systems (from the uncertainty perspective).…”

Section: Introductionmentioning

confidence: 99%

Random matrix based uncertainty model for complex robotic systems

2014 IEEE International Conference on Robotics and Automation (ICRA)

Alamdari

Das

et al. 2014

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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.

A Random Matrix Approach to Manipulator Jacobian

Volume 3: Nonlinear Estimation and Control; Optimization and Optimal Control; Piezoelectric Actuation and Nanoscale Control; Ro

Alamdari

Krovi

2013

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.