Algebraic path-planning of 6R/P Manipulators

6R/P manipulators are robots with 6 joints and for which each joint has only one degree of freedom and are either rotational or prismatic. They are among the most common robots in industrial setups. In the industry we often deal with serial manipulators. The most commonly studied manipulators are those that are purely rotational. The majority of inverse kinematics methods only deal with specific type of 6R (i.e. purely rotational jointed) manipulators. Algorithmic industrial applications (as opposed to manual applications where a human worker programs the robot manually) will only work if the kinematic mapping and the inverse kinematic of the robot is known. In this project, we would like to use and extend known inverse kinematic algorithms from 6R manipulators and develop new algorithms to analytically solve inverse kinematics of general 6R/P serial manipulators. In the study of the inverse kinematic we specifically want to extend and develop on the HUPF algorithm which is known to work well with 6R manipulators. This has a lot of advantage over numerical methods in solving inverse kinematics often used in the industry: Solutions are exact and are often obtained faster once one has a general analytic inverse kinematic formula. The configuration can be algebraically and analytically defined, which will allow us to take advantage of algebraic path-planning. The second phase of the project is developing new techniques in algebraic path-planning of 6R/P manipulators which is made possible from understanding the configuration space from closed form inverse kinematic solutions. This will have a significant advantage over random based path-planning which is mainstream both in academic research and industrial applications. We know that for specific 6R manipulators even a hybrid random-based and analytic/algebraic planner is more advantageous than pure random-based planner. We will use algebraic and geometric methods to device an efficient path planner for 6R/P manipulators.

Manipulators (robots) with 6 joints are very common in the industry, in fact they the most widely used robots. A common structure are manipulators with 6 joints that are either rotational or prismatic (6R/P e.g. a crane used in construction). The reason why we are very interested in robots with at least 6 joints, is their reachability in workspace. A common problem we face in industrial application is the inverse kinematics problem. Inverse kinematics is a non-trivial problem that asks for the configurations of the joints given the pose of a robot. There are many inverse kinematic algorithms developed so far, but most of the ones that are used in industrial applications have a numerical approach. Numerical algorithms are fast but there are some disadvantages. Exact analysis of the robot's workspace can best be done using symbolic and algebraic methods. We investigate the HuPf algorithm which was proven to work for 6R manipulators and extend this algorithm for 6R/P manipulators. We provide all linear spaces for all setups of 6R/P structure that is needed in the initial step of the HuPf algorithm reducing the preprocessing run-time, thus giving us an algorithm that has comparable runtime with numerical approach. The runtime is significantly better at the vicinity of a robots singularity where numerical approaches are often unstable. Furthermore, the algorithm provides all exact solutions of the inverse kinematic problem (of a non-singular pose) as opposed to the approximate and incomplete solutions provided by numerical methods. This project has lead the path for us to investigate different questions in robotics where exact inverse kinematic solution and kinematic analysis of industrial robot is necessary: e.g. exact path planning avoiding singularities, number of components of a singularity-free configurations space of a robot. These are topics that we are now investigating in a new international project.