A Tool to Solve Nonlinear Algebraic Equations Systems

Velez-Lopez, Gerardo C.; Hernandez-Martinez, L.; Diaz-Arango, G.; Vázquez-Leal, H.

doi:10.1109/iceee.2019.8884552

Cited by 1 publication

(2 citation statements)

References 6 publications

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“…The spherical path tracking of trajectories is complemented by the predictor–corrector algorithm, which helps follow the homotopic path without falling into discontinuities [ 22 , 23 , 24 , 42 ]. The predictor algorithm is used to generate the next point close to the homotopic trajectory

such that the intersection between the hypersphere and the y curve is achieved; in this work, the corrector was implemented with Broyden’s method [ 24 , 43 ], and the intersection between the hypersphere and the

curve is achieved. Figure 4 shows the predictor–corrector algorithm where

is the center of the hypersphere

and

represents the radius of the hypersphere.…”

Section: Path Planning Using Homotopy-based Formulationsmentioning

confidence: 99%

“…The HPPM-PRA represents a novel proposal for the homotopy continuation methods [ 22 , 23 , 24 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43 , 48 , 49 ] because it faces the problem of path planning by representing the configuration space (C-space) of the robot arm by using a system of algebraic equations and strategically allocated singularities, which are fundamental during the process of circumventing the obstacles. The proof of concept proved to be effective for implementation on real robots and prepares the way for implementation on scrolling robots in 3D configuration spaces.…”

Section: Conclusion and Future Workmentioning

confidence: 99%

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A Novel Collision-Free Homotopy Path Planning for Planar Robotic Arms

Velez-Lopez

Vázquez-Leal

Hernandez-Martinez

et al. 2022

Sensors

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Achieving the smart motion of any autonomous or semi-autonomous robot requires an efficient algorithm to determine a feasible collision-free path. In this paper, a novel collision-free path homotopy-based path-planning algorithm applied to planar robotic arms is presented. The algorithm utilizes homotopy continuation methods (HCMs) to solve the non-linear algebraic equations system (NAES) that models the robot’s workspace. The method was validated with three case studies with robotic arms in different configurations. For the first case, a robot arm with three links must enter a narrow corridor with two obstacles. For the second case, a six-link robot arm with a gripper is required to take an object inside a narrow corridor with two obstacles. For the third case, a twenty-link arm must take an object inside a maze-like environment. These case studies validated, by simulation, the versatility and capacity of the proposed path-planning algorithm. The results show that the CPU time is dozens of milliseconds with a memory consumption less than 4.5 kB for the first two cases. For the third case, the CPU time is around 2.7 s and the memory consumption around 18 kB. Finally, the method’s performance was further validated using the industrial robot arm CRS CataLyst-5 by Thermo Electron.

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