Optimal Force Generation for an Underconstrained Planar Cable Robot

This paper presents a planar, underconstrained cable robot designed to operate on the vertical face of overhead roadway signs. The cables that actuate the robot extend over a set of rotatable pulley arms mounted at the top corners of the sign. The redundant degrees of freedom due to the pulley arms allow for improved force generation ability of the robot at all desired locations on the sign. Redundancy is resolved by optimizing the anisotropic force generated in a desired direction. There are four distinct solution regimes dependent on the desired force angle. Of the four solution regimes, two are constraint-bound solutions for each cable force and the complementary cable angle based on monotonicity analysis. The two additional solutions are constraint-bound in the cable angles resulting in a fixed geometry, and the well-known attainable force set solution is applied.