Robot Manipulator Redundancy Resolution
7 Feedback-Aided Minimum Joint Motion
Kinematic redundancy can be obtained when a robot manipulator possesses more DOF than the minimum number required to execute a given end-effector task. If a robot manipulator is redundant, the inverse-kinematics problem may admit infinite solutions. How to obtain the required optimal solution, that is, the redundancy resolution problem, is an appealing and significant topic in robotics areas. In the past, many redundancy resolution schemes have been presented, and they can be divided into two main categories; that is, globally optimal control of redundancy and local/instantaneously optimal control of redundancy. The globally optimal concept and method were originally suggested by Whitney, and the early effective global schemes were presented by Uchiyama et al. and Nakamura et al. The global optimal schemes can generate the global optimal solutions, but they require a large amount of computation and are not suitable for real-time kinematic resolution. The detailed discussion can be referred to . Thus, the local/instantaneously optimal control schemes are widely investigated and used in robotics areas. The classic local optimal solution is pseudoinverse-type formulation, which is investigated in Chapter 1; that is, one minimum-norm particular solution plus a homogeneous solution. Based on such a pseudoinverse-type solution, many optimization performance criteria have been exploited in terms of manipulator configurations and interaction with the environment, such as joint-limits avoidance, singularity avoidance, manipulability enhancement, and obstacle avoidance. Recent research shows that the solutions to redundancy resolution problems can be enhanced by using optimization techniques based on quadratic program (QP) methods. Compared with the classic pseudoinverse-based solutions, such QP-based methods do not need to compute the inverse of the Jacobian matrix, and are readily to deal with the inequality and/or bound constraints. Thus, new interests in QP-based methods have been generated. In , considering the physical limits, Cheng et al. presented a compact QP method to resolve the constrained kinematic redundancy problem. As a specific example in , a repetitive motion planning (RMP) scheme was presented to illustrate the effectiveness of the compact QP method. Note that such an RMP scheme is based on Euclidean norm (or two-norm), and used to remedy the non-repetitive problem of the closed end-effector path (which is different from the path tracked in this chapter). The two-norm was widely used because of its analytical tractability, but minimizing the two-norm solution was not an ideal choice. Thus, some researchers began to investigate the optimization schemes based on the infinity norm and minimizing the infinity norm implied the determination of a minimum-effort solution as opposed to the minimum-energy criterion associated with the Euclidean norm. The torque-level and acceleration-level optimization schemes have also been investigated. It is worth pointing out that various criteria are exploited to optimize different objectives according to the requirements in general.