Kinematic Control of Redundant Robots with Online Handling of Variable Generalized Hard Constraints

TL;DR

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.

Abstract

We present a generalized version of the Saturation in the Null Space (SNS) algorithm for the 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. The proposed algorithm can be viewed as a generic platform that is easily applicable to any robotic application in which robots operate in an unstructured environment and online handling of joint and Cartesian constraints is critical.

Figures (10)

• Figure 1: The KUKA LWR IV robot used for experimental evaluation. The world frame is placed on the lab floor. The desired end-effector task, the initial (solid orange), intermediate (shaded blue), and final (shaded orange) robot configurations of the first experiment are shown.
• Figure 2: The task scaling factor associated with each constraint is computed in \ref{['scaling_factor']}. The factor is maximum (equal to 1 for the original task) when the corresponding velocity falls within the admissible interval, i.e., $b_{min,h} \leq \dot{a}_h \leq b_{max,h}$. In all other cases, the scaling factor is less than 1, and the constraint becomes more critical as the associated velocity moves further away from the boundaries of the interval.
• Figure 3: Simulation. The 6R planar arm is shown in its initial (black) and final (gray) configurations. The robot joints (and the end effector) are represented by red circles. The desired end-effector path is the blue line, to be traced from right to left. The Cartesian position bounds are indicated by the two dashed red lines. The dotted green lines are the paths of the chosen control points during task execution.
• Figure 4: Simulation. The end-effector $x$ and $y$ position errors and the associated task scaling factor.
• Figure 5: Simulation. Evolution of the position and velocity of the joints during task execution. The bounds on the joint motion are indicated by the dashed grey lines.