Stability analysis for set-based control within the singularity-robust multiple task-priority inverse kinematics framework

Abstract

Abstract-Inverse kinematics algorithms are commonly used in robotic systems to accomplish desired behavior, and several methods exist to ensure the achievement of several tasks simultaneously. The multiple task-priority inverse kinematics framework allows tasks to be considered in a prioritized order by projecting task velocities through the nullspaces of higher priority tasks. This paper extends this framework to handle setbased tasks, i.e. tasks with a range of valid values, in addition to equality tasks, which have a specific desired value. Examples of such tasks are joint limit and obstacle avoidance. The proposed method is proven to ensure asymptotic convergence of the equality task errors and the satisfaction of all high-priority set-based tasks. Simulations results confirm the effectiveness of the proposed approach.

Set-based Line-of-Sight (LOS) path following with collision avoidance for underactuated unmanned surface vessel

“…If the USV is outside the radius R m , path following is always active. However, in agreement with the method in [18], we allow the path following mode to be active inside R m under the condition that this will increase or maintain the current distance between the obstacle center and the USV, i.e. iḟ σ ≥ 0 with u = u pf and ψ = ψ pf .…”

“…These two different scenarios are considered the two modes of the system, and we will in the following, based on the set-based control approach [18], develop a method for switching between these two. Note that this approach can be used with any combination of methods for path following and collision avoidance and is not limited to the collision avoidance approach presented in the previous subsection.…”

“…Set-based tasks are relevant for the collision avoidance problem because a set-based task has a valid interval of values rather than an exact desired value, and collision avoidance may thus be considered as a set-based task defined as the distance between the USV and obstacle where the valid interval of the task has a lower bound of some minimum safe distance. The method presented in [17], [18] is, however, developed for fully actuated and redundant systems, and thus it cannot be directly applied to an underactuated surface vessel.…”

“…To achieve this, we utilize recent results that makes it possible to incorporate set-based tasks into a well-known prioritized task guidance framework. This method is presented for a general robotic system in [17], [18] and is experimentally validated in [19]. Set-based tasks are relevant for the collision avoidance problem because a set-based task has a valid interval of values rather than an exact desired value, and collision avoidance may thus be considered as a set-based task defined as the distance between the USV and obstacle where the valid interval of the task has a lower bound of some minimum safe distance.…”

“…Firstly, this paper suggests using set-based theory to satisfy two objectives: Collision avoidance and path following. The approach is adapted to the underactuated USV by switching between two predefined guidance laws rather than combining them using the Null-Space-Based Inverse Kinematics approach for fully actuated systems as in [17], [18]. The guidance laws, if satisfied, will ensure path following and collision avoidance respectively.…”