Robust Trajectory Planning of Under-Actuated Cable-Driven Parallel Robot with 3 Cables

Abstract

Cable-driven parallel robots (CDPRs) are under-actuated if they use a number of cables smaller than the degrees of freedom (DoF) of the end-effector (EE). For these robots, the constraint deficiency on the EE may lead to undesirable EE oscillations along the path that it is supposed to track. This paper proposes a trajectory-planning method for underactuated CDPRs which is robust against dynamic-model uncertainties or parameter variation, aiming at minimizing EE oscillations along a prescribed path. Oscillation reduction and robustness are achieved by means of Zero-Vibration Multi-Mode Input Shaping and Dynamic Scaling of a reference trajectory. Simulation results show the effectiveness of the method on a 3-cable 6-DoF robot.

Natural Oscillations of Underactuated Cable-Driven Parallel Robots

“…In order to highlight the interest of the modelling strategy proposed in this paper in a robotic context, a potential application example is presented in the following: the trajectory planning of a 6-DoF 4-cable UACDPR by a frequency-based method (i.e. Multi-Mode Zero-Vibration Input Shaping [16], [22]), experimentally compared with traditional methods. The robot under investigation has λ = 2 free pose components, and thus the trajectory of 4 EE dependent coordinates can be assigned for planning purposes 4 .…”

“…. , 4 are determined by setting to zero both summations inside the parentheses of the residual-amplitude equation [16], [22]:…”

“…Despite these drawbacks, the use of CDPRs with a limited number of cables may be favorable in several applications, in which a limitation of mobility is acceptable in order to enhance workspace accessibility or decrease mechanical complexity and robot cost [2]- [5]. Thus, the study of UACDPRs is attracting the interest of more and more researchers, who have dealt with their geometricostatic problems [6], [7], equilibrium stability analysis [8], [9], trajectory planning [1], [10]- [16], system parameter identification [17], and control [18]- [20].…”

“…The knowledge of natural oscillation frequencies of UACDPRs can be used in order to derive frequency-based trajectory planners based on periodic excitation [11] or input-shaping [12], [14]- [16]: these planners limit oscillations, and are real-time capable, as opposed to restto-rest trajectory planners [1], which can completely stop a UACDPR EE after a point-to-point motion, but needs to be computed off-line (and are not frequency-based). Additionally, natural oscillation frequencies may also be exploited for optimal robot design [21].…”

“…1) A novel unified technique is proposed for the computation of the natural oscillation frequencies of UACDPRs with a generic number n of cables (1 < n < 6), a generic geometry, and subject to a generic external wrench. Previous works only analyzed specific architectures, such as 2-cable 3-DoF UACDPRs [11], [12] and 3-cable 6-DoF UACDPRs [15], [16], or an approximation of a 4-cable 6-DoF UACDPR with two 2-cable 3-DoF UACDPRs [14]. Our approach allows an easy selection of the EE residual DoFs and the opportunity of easily switching between a selection and another, so that representation singularities may always be avoided in the formulation of the internal dynamics; the subsequent natural frequency computation is performed with a well-known tool, namely linearizing the internal dynamics about an equilibrium configuration.…”