| Quick, precise adaptive control of serial multi-link systems is important for many applications: satellite servicing, space station assembly and maintenance by free-flying robots, underwater exploration by mobile underwater robots and microsurgery by micro-hyper-redundant manipulators. Various modeling and control techniques have been developed but they are often cumbersome, computationally complex, and do not easily handle addition or deletion of rigid bodies from the manipulator system. A new task space adaptive controller and system concatenation technique has just been designed that makes on-line modular control possible; however, it requires the complicated formulation and computationally expensive inversion of various Jacobian matrices.; A spatial operator algebra framework has recently been developed for modeling and control of serial manipulators. This thesis uses spatial operator algebra to obtain new results in adaptive control of n-link serial manipulators. Specifically, order ({dollar}{lcub}cal N{rcub}{dollar}), where {dollar}{lcub}cal N{rcub}{dollar} is the total number of degrees of freedom in the system, recursive solutions to the Jacobian inverse and Jacobian pseudoinverse are formulated. These solutions address the special cases of singularities and redundant degrees of freedom. A task space inverse dynamics controller that takes advantage of the efficient inverse Jacobian solutions is presented in spatial operator algebra. The controller is also generalized to deal with manipulators with some unactuated joints (such as a mobile base robot and rigid element approximations of robots with link flexibility). The effectiveness of these new solutions is successfully demonstrated in simulation examples on serial rigid link manipulators with a fixed base, a mobile base, redundant degrees-of-freedom, and some unactuated joints. |
