On Stiffness Regulators with Dissipative Injection for Robot Manipulators

Abstract

The stiffness controller proposed by Salisbury is an interaction control strategy designed to achieve a desired form of static behavior as regards the interaction of a robot manipulator with the environment. The main idea behind this approach is the simulation of a multidimensional linear spring -or linear elastic material -using the difference between the actual position of the end-effector and a constant position (relaxed point), multiplied by a constant stiffness matrix. In this paper, this idea is generalized with the objective of proposing a controller structure that includes a family of stiffness models based on the idea of linear elastic materials. The new controller structure also includes a damping term in order to have control over energy dissipation, as well as a term added for the purpose of compensating the gravity forces of the links. The stability analysis of the proposed controller was performed in the Lyapunov sense. The new stiffness controller is presented as a case study and compared to other cases, such as the Salisbury controller (Cartesian PD) and the tanh-tanh controller. Experimental results using a three degrees-offreedom direct-drive robot for the evaluation of controllers in a constrained motion task are presented.

A generalised proportional-derivative force/vision controller for torque-driven planar robotic manipulators

“…. , m, represents the stiffness matrix and x e ∈ R m is the location of the environment into the robot task-space [5]. In order to achieve the control objectives stated in (17) - (18), our proposal is a generalised version of the energy shaping methodology [25] with the following proportionalderivative structure…”

“…Some examples of control algorithms for robot-environment interaction tasks are presented in [4], as a direct force regulator, or in [6,26], as a hybrid force/position controller. On the other hand, indirect force controllers are presented in [5], based on the stiffness of the environment, or in [8,13], based on the mechanical impedance that characterizes such interaction. Now, when combining or merging information coming from force/torque sensors and vision systems into the same control structure, some technical difficulties arise because of the different kind of data from each sensor.…”

An adaptive stiffness control scheme for robot manipulators in task-space

“…where q,q,q ∈ R n are the joint position, velocity and acceleration vectors, respectively, M(q) ∈ R n×n is the inertia matrix, C(q,q)q ∈ R n is the vector of centripetal and Coriolis torques, and g(q) ∈ R n is the vector of gravitational torques. The vector of control torques is τ ∈ R n , J(q) ∈ R m×n represents the Jacobian matrix of the manipulator, and f e ∈ R m is the interaction force vector [15]. For simplicity, the interaction forces can be modeled as…”

“…This scheme use the difference between the position of the end-effector and a constant position, multiplied by a stiffness matrix that represents the environment, so the controller reproduces the behavior of a linear elastic material [13,14]. The stiffness control problem was recently addressed in [15], where a family of stiffness controllers in task-space is proposed and the corresponding Lyapunov stability analysis is presented; and in [16], where a saturating stiffness control scheme for robots with bounded inputs is proposed.…”

A generalized adaptive stiffness control scheme for robot manipulators with bounded inputs

“…Constrained‐motion applications are those where a robot is in contact with the environment, whereas unconstrained‐motion applications are those where a robot is freely moving [4,5]. Force regulation or the constrained‐motion control problem has been addresed using direct and indirect force control algorithms such as explicit force control [6,7], hybrid force‐position control [8,9], impedance [5,10], or stiffness control [11,12].…”