Verimli bir ters dinamik yöntemi ile gerçek zamanlı fiziksel hareket kontrolü

Realistic character animations can be obtained using motion capture techniques. However, these captured motions can be recorded only for predetermined scenarios. A virtual character can have infinite variety of physical interactions with the virtual world, and it is not possible to anticipate all these interactions and record appropriate motions. But in real life when people interact with the surrounding environment, their motions are generated as a result of physics laws. In physics based animation studies, it is aimed that the reaction movements of the characters in the virtual environment occur in a natural way according to the laws of physics. In order to generate movements naturally, a simplified physical model needs to be controlled only by applying joint torques. These joint torques are calculated by benefiting from studies in fields such as robotics, biomechanics and physics. In order to be used in real-time applications, these calculations should be performed with very low processing costs, even for multi-body systems with very high degrees of freedom. In the literature, studies on physics-based animation can be grouped under two main titles: local controllers and equations of motion based controllers. The most commonly used local controller is the Proportional Derivative controller because of its simplicity of integration and problem modeling. One of the main drawbacks of local controllers is the need to tune gain parameters for each movement and character manually. Moreover they are not quite stable at the speeds required for real-time applications. In equations of motion based methods, modeling the problem and integration are more complex. However, these methods generate better results which are more stable than the results of local methods. Inverse dynamics constitutes the core component of equations of motion based methods. In physics based animation, Newton-Euler and Euler-Lagrange methods are used for inverse dynamics calculations. While Newton-Euler method is used to calculate the torques iteratively, Euler-Lagrange method is often used to obtain the analytical equations of motion needed for optimization problems. In this thesis, we obtained generalized equations of motion for multi-body systems in 3D space, whose orientations are represented by quaternions and consisting of rotational joints with 3 degrees of freedom, by using Kane's method. During this study, we have observed that for complex multibody systems, it is not feasible to calculate the inverse dynamics solution analytically neither by hand nor by using symbolic programming from these equations of motions. In order to be usable in real-time applications, we derived a recursive inverse dynamics algorithm from these equations. This algorithm is equivalent to recursive Newton-Euler algorithms, which are often used in physics based animation applications. Unlike other studies, since we obtain this algorithm from an analytical equation, we have introduced an integrated approach that can be used for both motion planning and motion generation as well as for inverse dynamics. We tested the results of our method in different scenarios and observed that for all scenarios our method produces stable results even at large timesteps. We also compared our method with some of the widely used methods in the literature.