Hierarchical Impedance-Based Tracking Control of Kinematically Redundant Robots

The control of a robot in its task space is a standard approach nowadays. If the system is kinematically redundant with respect to this goal, one can even execute additional subtasks simultaneously. By utilizing null space projections, for example, the whole stack of tasks can be implemented within a strict task hierarchy following the order of priority. One of the most common methods to track multiple task-space trajectories at the same time is to feedback-linearize the system and dynamically decouple all involved subtasks, which finally yields the exponential stability of the desired equilibrium. In this article, we provide a hierarchical multi-objective controller for trajectory tracking that ensures both asymptotic stability of the equilibrium and a desired contact impedance at the same time. In contrast to the state of the art in prioritized multi-objective control, feedback of the external forces can be avoided and the natural inertia of the robot is preserved. The controller is evaluated in simulations and on a standard lightweight robot with torque interface. The approach is predestined for precise trajectory tracking where dedicated and robust physical-interaction compliance is crucial at the same time.

I. Introduction

The definition and execution of tasks in the operational (or task) space is one of the most common approaches in robotics. While this strategy applies to both kinematic and force–torque control, especially the latter one is getting more and more important in the emerging field of physical human–robot interaction these days. If the robot is kinematically redundant with respect to the given task, it is possible to perform additional subtasks simultaneously as exemplified in Fig. 1. A common approach is to execute them in a prioritized manner by means of null space projections that have already been introduced to robotics decades ago [1]–[3] and have become standard tools since. One can ensure that lower priority subtasks do not disturb the execution of more important ones. To stay with the example in Fig. 1, one could assign a task hierarchy with safety-critical objectives such as collision avoidance having high priority. As a result, subtasks with lower priorities, e.g., the optimization of the joint configuration, would consequently not compromise safety.