Rigid–flexible interactive dynamics modelling approach

Abstract

Dynamics modelling of multi-body systems composed of rigid and flexible elements is elaborated in this article. The control of such systems is highly complicated due to severe underactuated conditions caused by flexible elements and an inherent uneven non-linear dynamics. Therefore, developing a compact dynamics model with the requirement of limited computations is extremely useful for controller design, simulation studies for design improvement and also practical implementations. In this article, the rigid-flexible interactive dynamics modelling (RFIM) approach is proposed as a combination of Lagrange and Newton-Euler methods, in which the motion equations of rigid and flexible members are separately developed in an explicit closed form. These equations are then assembled and solved simultaneously at each time step by considering the mutual interaction and constraint forces. The proposed approach yields a compact model rather than a common accumulation approach that leads to a massive set of equations in which the dynamics of flexible elements is united with the dynamics equations of rigid members. The proposed RFIM approach is first detailed for multi-body systems with flexible joints, and then with flexible members. Then, to reveal the merits of this new approach, few case studies are presented. A flexible inverted pendulum is studied first as a simple template for lucid comparisons, and next a space free-flying robotic system that contains a rigid main body equipped with two manipulating arms and two flexible solar panels is considered. Modelling verification of this complicated system is vigorously performed using ANSYS and ADAMS programs. The obtained results reveal the outcome accuracy of the new proposed approach for explicit dynamics modelling of rigid-flexible multi-body systems such as mobile robotic systems, while its limited computations provide an efficient tool for controller design, simulation studies and also practical implementations of model-based algorithms.

Cooperative Object Manipulation by a Space Robot with Flexible Appendages

“…So, the initial condition of the simulation study is stated in Table 3 which is the same for the two cases. It should be noted that the extracted dynamics model of space robot was verified by [4,5]. As mentioned before, two cases of implementation of the extended MIC law are studied in simulations based on the designed trajectories, that is, CASE-I for the designed MTT and CASE-II for the circular path which has the radius of 15 m. These maneuvers are important cases since flexible modes are stimulated due to on-off nature of actuating forces in the first one, and centripetal accelerations in the second one.…”

“…This operation was done by the defined generalized variable of the robot base which is shown in Figure 3. Assuming a rigid system (without FSP), the original form of the MIC law can successfully complete the object manipulation task based on the planned path with negligible errors [4,5]. Although the object manipulation task is successfully done in this case with FSP too, it would not be succeeded if the considerations in path designing such as a constant speed for the robot base are not taken into account, because the simulation was stopped after the flexible solar panels had been fractured.…”

“…The kinetic energy as the virtual work of the forces acting on the body is written in terms of the coupled sets of reference and elastic coordinates [31]. Then, the motion's equations of the flexible members can be obtained as [4,5] …”

“…Then, we solve the equations of motion for the flexible subsystem considering these inputs. The obtained constraint forces are attained as the outputs which will be exerted on the mobile base of the space robot as estimated disturbance forces, [4,5]. Considering (6), the generalized forces due to the stimulation of the flexible members which are applied on the rigid subsystem as the modification term or the constraint force or Q flex.…”

“…The required settling time for vibration of such parts may delay the operation and so conflicts with increasing time efficiency of the system. This conflict of high speed and high accuracy during any operation makes these robots a disputative research problem [2][3][4][5].…”