Summary This paper involves the study of a general formulation and numerical solution for the dynamic load‐carrying capacity of a mechanical manipulator with elastic links. The approach presented in this article is based on an open‐loop optimal control. This method results from the Pontryagin minimum principle, which yields a 2‐point boundary value problem. The indirect method has been exploited to extract the optimality conditions. The dynamic equations of motion for this system have been obtained by means of the Gibbs‐Appell formulation and by applying the assumed modes method. The elastic characteristics of the members have been modeled based on the Timoshenko beam theory and its associated mode shapes. The aim of this research is to calculate the maximum‐allowed load that a mechanical manipulator with flexible links can carry while traversing an optimal path. At the end, to evaluate the proposed method, we made a comparison between the simulation results obtained from the presented model and the experimental results obtained from a manipulator with 2 flexible links. The comparison between the simulation and empirical data confirms the credibility of the presented method in computing the dynamic load‐carrying capacity and controlling the point‐to‐point motion of the considered 2‐link flexible manipulator.

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SUMMARYThis study deals with the problem of trajectory tracking of wheeled mobile robots (WMR's) under non-holonomic constraints and in the presence of model uncertainties. To solve this problem, the kinematic and dynamic models of a WMR are first derived by applying the recursive Gibbs–Appell method. Then, new kinematics- and dynamics-based multivariable controllers are analytically developed by using the predictive control approach. The control laws are optimally derived by minimizing a pointwise quadratic cost function for the predicted tracking errors of the WMR. The main feature of the obtained closed-form control laws is that online optimization is not needed for their implementation. The prediction time, as a free parameter in the control laws, makes it possible to achieve a compromise between tracking accuracy and implementable control inputs. Finally, the performance of the proposed controller is compared with that of a sliding mode controller, reported in the literature, through simulations of some trajectory tracking maneuvers.

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