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The main goal of this paper is to present an automatic approach for the dynamic modeling of the oblique impact of a multi-flexible-link robotic manipulator. The behavior of a multi-flexible-link system confined inside a closed environment with curved walls can be completely expressed by two distinct mathematical models. A set of differential equations is employed to model the system when it has no contact with the curved walls (Flight phase); and a set of algebraic equations is used whenever it collides with the confining surfaces (Impact phase). In this article, in addition to the Assumed Mode Method (AMM), the Euler-Bernoulli Beam Theory (EBBT), and the Newton's kinematic impact law, the Gibbs-Appell (G-A) formulation has been employed to derive the governing equations in both phases. Also, instead of using 3 Â 3 rotational matrices, which involves lengthy kinematic and dynamic formulations for deriving the governing equations, 4 Â 4 transformation matrices have been used. Moreover, for the systematic modeling of flexible multiple links through the space, two virtual links have been added to the n real links of a manipulator. Finally, two case studies have been simulated to demonstrate the validity of the proposed approach.

This paper has focused on the dynamic analysis of mechanisms with closed-loop configuration while considering the flexibility of links. In order to present a general formulation for such a closed-loop mechanism, it is allowed to have any arbitrary number of flexible links in its chain-like structure. The truncated assumed modal expansion technique has been used here to model link flexibility. Moreover, due to the closed nature of the mentioned mechanism, which imposes finite holonomic constraints on the system, the appearance of Lagrange multipliers in the dynamic motion equations obtained by Lagrangian formulation is unavoidable. So, the Gibbs-Appell (G-A) formulation has been applied to get rid of these Lagrange multipliers and to ease the extraction of governing motion equations. In addition to the finite constraints, the impulsive constraints, which originate from the collision of system joints with the ground, have also been formulated here using the Newton's kinematic impact law. Finally, to stress the generality of the proposed formulation in deriving and solving the motion equations of complex closed-loop mechanisms in both the impact and non-impact conditions, the computer simulation results for a mechanism with four flexible links and closed-loop configuration have been presented.

In the present work, a novel method is devised for controlling an uncertain wheeled mobile robot (WMR) in a desired path. To achieve this objective, an optimal and robust control system with adaptive gains is combined to benefit from the advantages of both methods. In fact, applying this controller not only controls a nonlinear system robustly against uncertainties and external disturbances, but also optimizes a quadratic cost function. Also, since the upper bound of uncertainty is determined by an adaptive law, it does not need to be adjusted manually. To ensure the designed controller's finite time stability, Lyapunov theory is used. Finally, to illustrate the effectiveness of the proposed control method, a case study involving a WMR is presented. By comparing the results of this approach with those of an adaptive sliding mode control (ASMC), it is shown that the proposed controller uses less control effort, relative to the ASMC controller, to stabilize the uncertain WMR in the presence of external disturbances.

This study uses a comprehensive control approach to deal with the trajectory tracking problem of a two-flexible-link manipulator subjected to model uncertainties. Because the control inputs of two-flexible-link manipulators are less than their state variables, the proposed controller should be able to tackle the stated challenge. Practically speaking, there is only a single control signal for each joint, which can be used to suppress link deflections and control joint trajectories. To achieve this objective, a novel optimal robust control scheme, with an updated gain under the adaptive law, has been developed in this work for the first time. In this regard, a nonsingular terminal sliding mode control approach is used as the robust controller and a control Lyapunov function is used as the optimal control law, to benefit from the advantages of both methods. To systematically deal with system uncertainties, an adaptive law is used to update the gain of nonsingular terminal sliding mode control. The advantage of this approach over the existing methods is that it not only can robustly and stably control an uncertain nonlinear system against external disturbances but also can optimally solve a quadratic cost function (e.g. minimization of control effort). The Lyapunov stability theory has been applied to verify the stability of the proposed approach. Moreover, to show the superiority of this method, the computer simulation results of the proposed method have been compared with those of an adaptive sliding mode control scheme. This comparison shows that the presented approach is capable of optimizing the control inputs while achieving the stability of the examined two-flexible-link manipulator in the presence of model uncertainties and external disturbances.

In this article, a recursive approach is used to dynamically model a tree-type robotic system with floating base. Two solution procedures are developed to obtain the time responses of the mentioned system. A set of highly nonlinear differential equations is employed to obtain the dynamic behavior of the system when it has no contact with the ground or any object in its environment (flying phase); and a set of algebraic equations is exploited when this tree-type robotic system collides with the ground (impact phase). The Gibbs–Appell (G–A) formulation in recursive form and the Newton’s impact law are applied to derive the governing equations of the aforementioned robotic system for the flying and impact phases, respectively. The main goal of this article is a systematic algorithm that is used to divide any tree-type robotic system into a specific number of open kinematic chains and derive the forward dynamic equations of each chain, including its inertia matrix and right-hand side vector. Then, the inertia matrices and the right-hand side vectors of all these chains are automatically integrated to construct the global inertia matrix and the global right-hand side vector of the whole system. In fact, this work is an extension of Shafei and Shafei (2016, “A Systematic Method for the Hybrid Dynamic Modeling of Open Kinematic Chains Confined in a Closed Environment,” Multibody Syst. Dyn., 38(1), pp. 21–42.), which was restricted to a single open kinematic chain. So, to show the effectiveness of the suggested algorithm in deriving the motion equations of multichain robotic systems, a ten-link tree-type robotic system with floating base is simulated.