Collision Detection and Avoidance in Computer Controlled Manipulators (2018)

This dissertation tackles the problem of planning safe trajectories for computer controlled manipulators with two links and multiple degrees of freedom. There are two ways to look at safe trajectory planning. The first concerns itself with planning trajectories in empty space; obstacles enter into consideration only indirectly in that they determine what part of the maneuverable space is free. The second considers obstacles alone; free space considerations are of secondary importance. We show how these complementary views can be used to advantage in the safe trajectory planning problem. Obstacles are naturally described in cartesian space and trajectories in joint space. If obstacles and trajectories are both represented in one space, collision checks would not require the constant and expensive conversion between the two spaces. We show how it is possible to decompose the planning task so as to get the best of both cartesian space and joint space representations, and yet avoid the constant conversion overhead problem. We show how the principles of hierarchical decomposition can be used to reduce the complexity of the manipulator trajectory planning problem. Different strategies are used for maneuvering far away from obstacles and for maneuvering close to obstacles. A characterization of large chunks of empty space makes maneuvering far away from obstacles very easy. A characterization of obstacle configuration types simplifies planning of maneuvers close to obstacles. The key ideas in the representation that make it possible to realize the above claims are: 1) the identification of a hierarchy of abstraction spaces that permit simplified manipulator descriptions. These spaces make it possible to model the manipulator as two line segments, a single line segment, or incredibly as a point. 2) the identification of primitive trajectory types that make collision detection, trajectory hypothesis and modification numerically tractable. 3) the polyhedra-model of obstacles and the identification of one-time-only transformations on obstacles that significantly simplify trajectory planning. 4) a neat characterization of empty space. Empty space is approximated by easily describable entities called charts; the approximation is dynamic and under program control; the approximation can be selective, and thus it is easy to make incremental modifications to the charts. The thesis describes a model for collision detection and avoidance systems for computer controlled manipulators. The justification for the model lies in the computer implementations for 2D and 3D manipulator systems. These systems incorporate a significant portion of the model. The promising performance of the implementation makes fast collision avoiders a distinct possibility. The solution presented treats manipulators with a sliding joint, and permits the manipulator to transport objects which can be enclosed within the minimum bounding cylinder of the manipulator link. Modifications of the solution that permit handling of large objects are indicated. An extension of the solution that solves the problem for manipulators with only rotary joints is described. A consequence of the investigations into the collision detection and avoidance problem has been the identification of execution-time strategies for terminal phase motion. Guidelines have been presented for incorporating proximity sensors into the manipulator system.