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    Alexandr Klimchik

    ul. Universitetskaya 1, Innopolis, 420500 Russia
    Innopolis University


    Kulathunga G., Devitt D., Fedorenko R., Klimchik A. S.
    Any obstacle-free path planning algorithm, in general, gives a sequence of waypoints that connect start and goal positions by a sequence of straight lines, which does not ensure the smoothness and the dynamic feasibility to maneuver the MAV. Kinodynamic-based motion planning is one of the ways to impose dynamic feasibility in planning. However, kinodynamic motion planning is not an optimal solution due to high computational demands for real-time applications. Thus, we explore path planning followed by kinodynamic smoothing while ensuring the dynamic feasibility of MAV. The main difference in the proposed technique is not to use kinodynamic planning when finding a feasible path, but rather to apply kinodynamic smoothing along the obtained feasible path. We have chosen a geometric-based path planning algorithm “RRT*” as the path finding algorithm. In the proposed technique, we modified the original RRT* introducing an adaptive search space and a steering function that helps to increase the consistency of the planner. Moreover, we propose a multiple RRT* that generates a set of desired paths. The optimal path from the generated paths is selected based on a cost function. Afterwards, we apply kinodynamic smoothing that will result in a dynamically feasible as well as obstacle-free path. Thereafter, a b-spline-based trajectory is generated to maneuver the vehicle autonomously in unknown environments. Finally, we have tested the proposed technique in various simulated environments. According to the experiment results, we were able to speed up the path planning task by 1.3 times when using the proposed multiple RRT* over the original RRT*.
    Keywords: RRT*, iLQR, B-spline, OctoMap, ellipsoidal search space
    Citation: Kulathunga G., Devitt D., Fedorenko R., Klimchik A. S.,  Path Planning Followed by Kinodynamic Smoothing for Multirotor Aerial Vehicles (MAVs), Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 4, pp.  491-505
    Mikhel S. K., Klimchik A. S.
    The accuracy of the robot positioning during material processing can be improved if the deformation under the load is taken into account. A manipulator stiffness model can be obtained using various approaches which differ in the degree of detail and computational complexity. Regardless of the model, its practical application requires knowledge of the stiffness parameters of the robot components, which implies solving the identification problem.
    In this work, we consider a reduced stiffness model, which assumes that the manipulator links are rigid, while the joints are compliant and include both elasticities in the joints themselves and the elastic properties of the links. This simplification reduces the accuracy of the model, but allows us to identify the stiffness parameters, which makes it suitable for practical application. In combination with a double encoders measurement system, this model allows for real-time compensation of compliance errors, that is, the deviation of the real end-effector position from the calculated one due to the deformation of the robot under load.
    The paper proposes an algebraic approach to determining the parameters of the reduced model in a general form. It also demonstrates several steps that can be done to simplify computations. First, it introduces the backward semianalytical Jacobian computation technique, which allows reducing the number of operations for the manipulator with virtual joints. Second, it provides an algorithm for the calculation of the required intermediate matrices without explicit Jacobian calculation and using more compact expressions.
    To compare the proposed techniques with the experimental approach, the robot deformation under load is simulated and the tool displacement is estimated. It is shown that both approaches are equivalent in terms of accuracy. While the experimental method is easier to implement, the algebraic approach allows analyzing the contribution of each link in a reduced model of
    Keywords: robot stiffness, Jacobian evaluation, identification
    Citation: Mikhel S. K., Klimchik A. S.,  Stiffness Model Reduction for Manipulators with Double Encoders: Algebraic Approach, Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 3, pp.  347-360

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