Computational improvements of a multibody dynamic simulation algorithm applied to a landing event simulation of a flexible legged Europa lander

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Wachlin, Jacob T.
Costello, Mark
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Multibody dynamic simulation is critical to the design and analysis of many mechanical systems. Engineers use these simulations to understand the motion and loading conditions of systems of bodies. The field of dynamic simulation has been studied for decades and many methods exist for performing multibody dynamic simulations, each with its advantages and disadvantages. For example, some methods are more computationally expensive than others, and many methods naturally eliminate inter-body loads from calculations. This thesis focuses on a constrained coordinate method for developing multibody dynamic simulations which uses nonlinear control theory techniques in the constraint stabilization task. The constrained coordinate multibody dynamic simulation method considered in this thesis has been used to examine the performance of many systems. It has been used to model parafoil systems, articulated wing aircraft, and guided projectiles [1]. Within this method, each rigid body is simulated using a standard 6 degree-of-freedom model, with loads at connections between bodies calculated online to maintain properly constrained motion between the bodies. The method avoids the need to analytically derive a set of governing coupled differential equations for the system. In addition, it does not cancel out inter-body loads, which can be useful for engineering analysis. However, because the interbody loads must be calculated and applied online, and constrained degrees-of-freedom are not eliminated from the simulation, this method can be computationally expensive. This thesis makes significant computational improvements to this constrained coordinate multibody dynamic simulation algorithm. It first analyzes the algorithm to determine which sections scale most poorly with system size. It then suggests, analyzes, and tests methods to greatly reduce computation time within those problem sections. In particular, it shows how some matrix multiplication operations consist of a large number of multiplications by zero. Computation time is reduced by avoiding these trivial operations. In addition, it is shown how the joint numbering scheme determines the bandwidth of a matrix corresponding to a set of linear equations that must be solved within the constraint controller. When the bandwidth is reduced, banded linear system solvers can be used to reduce computation time. The bandwidth reduction here is shown to be equivalent to the standard NP-Complete bandwidth reduction problem. Approximate bandwidth reduction methods are shown to be effective at reducing computation time. A few token systems are developed to test the methods and it is noted that computation time in some cases is reduced by more than two orders of magnitude, opening up this technique for use in trade studies of the dynamics of large systems. Finally, these methods are applied to simulate the landing event dynamics of a proposed flexible legged lander for Europa. The reduced computation time enabled by the methods presented in this thesis allows for large Monte-Carlo simulation studies to be run in a reasonable amount of time. Systems with various levels of passive leg flexibility were modeled, as well as a system with basic active impedance control, and it was seen that flexible legs offer lower peak acceleration on impact, lower joint loads, and lower risk of rollover over a wide range of ground surface conditions, impact angles, and impact velocities. Flexible legs lowered peak lander acceleration by about 42% and 40% on simulated icy and snowy surfaces, respectively. Flexible legs were also able to virtually eliminate rollover risk when landing on those surfaces. On a simulated sandy surface with significantly higher damping, flexible legs reduced peak lander acceleration by about 31%. In addition, while landers with stiff legs rolled over in this sandy surface scenario about 35% of the time, landers with very flexible legs rolled over only 15.5% of the time.
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