Multi-rigid-body contact dynamics and haptic interaction for fixture loading planning

The thesis presents an approach to the fixture loading planning problem. That is, to plan the applied forces on the workpiece in order for it to be loaded into a manufacturing fixture. In our approach, a sequence of applied forces on the mass center of the workpiece is planned. The applied forces will push the workpiece to get in contact with all the locators. For this purpose, we developed a system with two engines, Motion Planning Engine and Dynamics Simulation Engine. Motion Planning Engine uses the current workpiece position as the input and generate its new velocity or the applied force on it. Dynamics Simulation Engine is a reverse, it generate the new position of the workpiece from the current position, velocity, and applied force on the workpiece. Dynamics Simulation Engine is the foundation of the whole system. The engine maintains a realistic dynamics scene in either automatic planning or haptic guided planning. It serves as an off-line verification of the planned motion so that the generated scheme can be ‘played’ with the engine. In this thesis, we developed a three-dimensional dynamics simulation engine based on an extension of the explicit time-stepping scheme and an application of the differential inclusion process introduced by J. J. Moreau. In the engine, we developed the contact propagation method for a general three-dimensional rigid-body system with multiple unilateral contacts without any bilateral constraints. We considered the general 3-dimensional case of smooth surfaces. We use a differential model of the kinematics of surface contact for contact point tracking. While the contact kinematics of general 3-dimensional i surfaces considerably increase the complexity of the dynamic analysis, the generalization to 3D would have to deal with the nonlinearity introduced by Coulomb’s friction law, compared to the 2D case where the friction force is essentially linear. No such a generalization is yet reported in the literature. The goal of Motion Planning Engine is to make the workpiece in contact with all the six locators. Here, the workpiece is initially at an arbitrary place with not contact with any locator. The planning follows a simple scheme of monotonously increase the number of contacts with locators. The sequence of locators to be contacted is assigned by the user in the beginning of the planning. The major effort is on the fine-motion planning of approaching a new contact while maintaining existed contacts. The difficulty comes when there are multiple contacts. Here we use a two-step scheme. First, finding the velocity of the workpiece that can approach the new locator while maintaining contacts with old locators. This can be formulated as a linear programming problem. Second, finding the applied force to realize such motion. This step is a central issue in the planning because for the rigid-body model, the solution to multiple frictional contacts is generally indeterministic. One possibility is jamming, that is, the applied force cannot move the workpiece even with less than six contacts. In this thesis, we will give criteria to determine whether the jamming will happen, and we will also derive an algorithm to generate the nonjamming applied force. We also developed a haptics guided planning system incorporating human interaction and force-feedback with a Phantom. With this system the user can either edit the automatically planned scheme if it is not satisfactory or generate the scheme manually in case the automatic planning fails.