Optimization of Actuator Forces in Cable-Based Parallel Manipulators Using Convex Analysis

Abstract-In this paper, we present a novel linear-program formulation that yields "optimally safe" (OS) tension distributions in parallel cable-driven robots by the introduction of a slack variable. The slack variable also enables explicit computation of a near-optimal, feasible starting point. This, in turn, enables rapid computation of the OS tension distributions. The formulation also contains a parameter that can be used to steer cable tensions toward desired regions of operation. We present static results from two simulated robotic systems that demonstrate the ability of our formulation to avoid tension limits. Simulated execution of highly dynamic trajectories on both systems demonstrates rapid-computation abilities. Furthermore, we present experimental results from a real robotic system that further validate the importance of safe tension distributions.Index Terms-Cable tension distributions, parallel cable-driven robots, parallel robots, redundant robots.

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“…Previous work has considered both g(f ) = f 1 [5] and g(f ) = f 2 [15], [17]. In the former case, the optimization becomes an LP.…”

Section: A Definition Of the Tension-distribution Problemmentioning

confidence: 99%

“…However, their methods do not extend to redundantly restrained systems. Hassan and Khajepour [17] use Dykstra's alternating-projection algorithm to find the minimum-norm tension distribution for a pair of simulated robotic systems. This is an iterative convex-optimization method that requires a large number of iterations to converge.…”

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confidence: 99%

Rapid Computation of Optimally Safe Tension Distributions for Parallel Cable-Driven Robots

et al. 2009

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“…Since each platform is driven by n-6 redundant cables, it is important that the tension be distributed among them according to kinematic and dynamic conditions so as to minimize the actuation power over all actuators (Hassan & Khajepour, 2008). It is desired to maintain the tension in the cables above a minimum threshold value τ min to limit cable sagging.…”

Section: Optimal Tension Distributionmentioning

confidence: 99%

Cartesian Control of a Cable-Driven Haptic Mechanism

Otis¹,

Duchaine²,

Billette³

et al. 2010

Advances in Haptics

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“…Three types of vector norms are generally used such as, 1-norm, 2-norm or ∞-norm. 2-norm or Euclidean length is preferred (Hassan and Khajepour, 2008) over the other two norms because it is more sensitive towards changes in larger force components. 1-norm is equally sensitive to all the force components and ∞-norm is only sensitive to the changes in the largest force component.…”

Section: Minimum Actuator Force Based Criteriamentioning

confidence: 99%

“…Several performance indices such as manipulability, isotropy, dexterity index, conditioning index, global conditioning index and global isotropy index have been defined by different researchers (Khatami & Sassani, 2002) to compare the performances of competing manipulator designs. In a recent study (Hassan & Khajepour, 2008) the actuator forces in a cable based parallel manipulator have been optimized using a minimum norm solution. Authors have used Dykstra's projection method to optimally distribute the actuator forces among the cables and the redundant limbs.…”

Section: Design Optimizationmentioning

confidence: 99%