Numerical approach of collision avoidance and optimal control on robotic manipulators

Collision-free optimal motion and trajectory planning for robotic manipulators are solved by a method of sequential gradient restoration algorithm. Numerical examples of a two degree-of-freedom (DOF) robotic manipulator are demonstrated to show the excellence of the optimization technique and obstacle avoidance scheme. The obstacle is put on the midway, or even further inward on purpose, of the previous no-obstacle optimal trajectory. For the minimum-time purpose, the trajectory grazes by the obstacle and the minimum-time motion successfully avoids the obstacle. The minimum-time is longer for the obstacle avoidance cases than the one without obstacle. The obstacle avoidance scheme can deal with multiple obstacles in any ellipsoid forms by using artificial potential fields as penalty functions via distance functions. The method is promising in solving collision-free optimal control problems for robotics and can be applied to any DOF robotic manipulators with any performance indices and mobile robots as well. Since this method generates optimum solution based on Pontryagin Extremum Principle, rather than based on assumptions, the results provide a benchmark against which any optimization techniques can be measured

Manipulability in trajectory tracking for constrained redundant manipulators via sequential quadratic programming

Trajectory tracking methods for constrained redundant manipulators are presented in this thesis, where the end-effector of a redundant serial manipulator has to track a desired trajectory while some points on its kinematic chain satisfy one or more constraints. In addition, two manipulability indexes are taken into account in order to optimize the trajectory. The first index is defined in terms of the geometric Jacobian of the manipulator in the constrained configuration. The second index is based on the constrained Jacobian, which maps velocities from joint space to task space, taking into account the holonomic constraints. Three methods for solving the trajectory tracking problem are discussed. The first two, kinematic control (KC) and quadratic programming (QP), are widely discussed in literature. The third, sequential quadratic programming (SQP), is a new approach, unlike KC or QP, has as advantages (despite some shortcomings) not explicitly depend on pseudoinverse Jacobian, derivative from the desired trajectory and linearization of indexes or constraints. A discussion of these three methods is presented in terms of tracking error, constraint violation, singularity distance, among others through experiments performed on a Baxter collaborative robot.Métodos de rastreamento de trajetória para manipuladores redundantes restritos são apresentados nesta tese, onde o efetuador de um manipulador serial redundante tem que rastrear uma trajetória desejada enquanto alguns pontos em sua cadeia cinemática satisfazem uma ou mais restrições. Além disso, dois índices de manipulabilidade são levados em consideração a fim de otimizar a trajetória para evitar singularidades. O primeiro índice é definido em função do jacobiano geométrico do manipulador na configuração restrita. O segundo índice é baseado no Jacobiano restrito, o qual mapeia velocidades no espaço das juntas para a espaço da tarefa, levando em conta as restrições holonômicas. Três métodos para resolver o problema de rastreamento de trajetória são discutidos. Os dois primeiros, controle cinemático e programação quadrática (QP), são amplamente discutidos na literatura. O terceiro, programação quadrática sequencial (SQP), é uma nova abordagem, diferentemente do controle cinemático ou QP, tem como vantagens (apesar de algumas deficiências) não depender explicitamente da pseudo-inversa de jacobianos, derivadas da trajetória desejada e linearização de índices ou restrições. Uma discussão desses três métodos é apresentada em termos de erro de rastreamento, violação da restrição, distância de singularidades, entre outros através de experimentos realizados em um robô colaborativo Baxter