Discrete-time Redundancy Resolution at the Velocity Level with Acceleration/Torque Optimization Properties

With reference to robots that are redundant for a given task, we present a novel and intuitive approach allowing to define a discrete-time joint velocity command that shares the same characteristics of a second-order inverse differential scheme, with specified properties in terms of joint acceleration or torque. Our main goal is to show how commands in the null space of the task can yield different locally optimal solutions, working only at the velocity control level. By following our general method, it is possible to obtain simple implementations of possibly complex robot control laws that (i) can be directly interfaced to the low-level servo loops of a robot, (ii) require less task information and on-line computations, (iii) are still provably good with respect to some target performance. The method is illustrated by considering the conversion into discrete-time velocity commands of control schemes for redundant robots that minimize the (weighted and/or biased) norm of joint acceleration or joint torque. The approach can be extended to auxiliary tasks, possibly organized with priority. Numerical simulations and experimental results are presented for the control of a 7R KUKA LWR IV robot.