Wrench Uncertainty Quantification and Reconfiguration Analysis in Loosely Interconnected Cooperative Systems

Abstract

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.

Matrix-Based Characterization of the Motion and Wrench Uncertainties in Robotic Manipulators

“…We show that random matrix theories can be used to systematically model the effect of these uncertainties with significantly less characterization efforts. Since limited available information is used in formulating the RMT-based model, it may provide lower fidelity compared to the parametric approaches in which all random entities are carefully modeled (see [47]). However, constructing these parametric models is not feasible in several complex systems and one may seek alternative approaches to appropriately model system variations.…”

“…Using the parametric formulation [47], we estimate the parameters of the RMT-based model when only some bounds on the parameters are given. Through an exhaustive evaluation we show that RMT-based model provide acceptable accuracy as far as system parameters remain in the known bounds.…”

“…. , m. We showed that the variances of the wrench vector elements can then be calculated as [13], [47]…”

“…While all configurations provide (approximately) the same mean wrench at the platform, the uncertainty profile is significantly different. See [47] for details on the uncertainty-based optimization of the system configuration. The idea is to investigate the effectiveness of the Gaussian product model in capturing the real system output in a cooperative system.…”

Wrench-Feasible Workspace of Mobile Cable-Driven Parallel Robots

“…A concept of CDPRs with base mobility is introduced in [15] for optimizing the orientation workspace and stiffness of the moving-platform. A similar system for optimizing the robot configuration in order to increase the position accuracy of the moving-platform is presented in [16]. A novel concept of Mobile Cable-Driven Parallel Robots (MCDPRs) was introduced in [17].…”