We present an efficient method for addressing online the inversion of differential task kinematics for redundant manipulators, in the presence of hard limits on joint space motion that can never be ...violated. The proposed Saturation in the Null Space (SNS) algorithm proceeds by successively discarding the use of joints that would exceed their motion bounds when using the minimum norm solution. When processing multiple tasks with priority, the SNS method realizes a preemptive strategy by preserving the correct order of priority in spite of the presence of saturations. In the single- and multitask case, the algorithm automatically integrates a least possible task-scaling procedure, when an original task is found to be unfeasible. The optimality properties of the SNS algorithm are analyzed by considering an associated quadratic programming problem. Its solution leads to a variant of the algorithm, which guarantees optimality even when the basic SNS algorithm does not. Numerically efficient versions of these algorithms are proposed. Their performance allows real-time control of robots executing many prioritized tasks with a large number of hard bounds. Experimental results are reported.
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.
•A method to convert in a discrete-time velocity law any second-order control scheme.•In redundant robots, preserves the original properties (minimum acceleration/torque).•Equivalence is obtained in all cases by a proper choice of a vector in the task null space.•Solutions are simple to implement and are interfaced directly to low-level controllers.•Validating simulations and experiments on a 7R KUKA LWR IV robot.
We present a generalized version of the Saturation in the Null Space (SNS) algorithm for task control of redundant robots when hard inequality constraints are simultaneously present both in the joint ...and in the Cartesian space. These hard bounds should never be violated, are treated equally and in a unified way by the algorithm, and may also be varied, inserted or deleted online. When a joint/Cartesian bound saturates, the robot redundancy is exploited to continue fulfilling the primary task. If no feasible solution exists, an optimal scaling procedure is applied to enforce directional consistency with the original task. Simulation and experimental results on different robotic systems demonstrate the efficiency of the approach.
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