Non-linear phase different control for precise output force of bi-articularly actuated manipulators

Abstract

Bi-articular actuators -actuator spanning two joints -play fundamental role in robot arms designed under the human musculoskeletal actuation paradigm. Unlike kinematic redundancy, actuator redundancy resulting from bi-articular actuation brings advantages such as increasing stability, reducing link's inertia, and decreasing non-linearity of the end-effector force with respect to the force direction. The traditional phase different control (PDC) resolves actuator redundancy on the basis of a linearized model derived from measured human muscle activity. Such linear model produces a non-zero error in calculation between a desired output force and necessary inputs. In this paper, the non-linear phase different control (NLPDC) is proposed to resolve actuator redundancy with no error. The maximum end-effector force of BiWi, bi-articularly actuated, and wire-driven arm, is measured using both PDC and NLPDC. When the robot arm moves towards singular configurations, the measured error in output force remains within the modeling error if using NLPDC, while such error increases significantly for PDC. Furthermore, unlike PDC, the proposed NLPDC allows design of joint stiffness and torque independently, reduction of necessary total muscle input force, and precise calculation of maximum output force.

Comparing Approaches for Actuator Redundancy Resolution in Biarticularly-Actuated Robot Arms

“…The muscle forces in the NLPDC are the same as PDC when they are null (0) or maximum [e m i and f m i for i = (1, 2, 3)]. Elsewhere, the muscle forces are calculated on the basis of the robot arm geometry as shown in [24], resulting in …”

“…The NLPDC is proposed to avoid the calculation error from end-effector force to input torques caused by the linearization process in the PDC [24].…”

“…These six approaches for redundancy resolution are all already present in the literature. Among these six approaches, three have been proposed by the authors, namely ∞-norm [23], NLPDC [24], and LP [25]. BiWi, a biarticularly actuated and wire-driven robot arm, is used to experimentally evaluate the maximum end-effector force achievable with the six methods.…”

Analytical study on increasing isotropy of intrinsic stiffness in manipulators through biarticular structure

“…It has been shown that, biarticular actuators dramatically increase the range of end effector impedance which can be achieved without feedback [13], increase the capability of path tracking and disturbance rejection, [14] allow for precise output force control [15], and improve balance control for legged robots without force sensors [16]. In addition, biarticularly actuated manipulators produce a maximum output force at the end effector in a more homogeneously distributed way [17].…”

“Load balance” control for a humanoid musculoskeletal arm in table tennis movement

“…Based on this discharge pattern, a Phase Different Control (PDC) was developed, where a linear muscle activation pattern is modeled based on the electromyography observations of human arm experiments [39]. Later on, the PDC method was improved to be Non-Linear Phase Different Control (NLPDC), which eliminates the error between the calculated muscle activation level and the desired force on the end-effector [40].…”