A Robot Manipulator With 16 Real Inverse Kinematic Solution Sets

Manseur, Rachid; Doty, Keith L.

doi:10.1177/027836498900800507

Cited by 42 publications

(30 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Indeed, 16 is the upper bound of number of solutions of any open-link spatial mechanism with six degrees of freedom. This number is a sharp bound-that is to say, it is achievable (see, for example, [65])-and is far superior to those obtained from a brute force elimination technique using Bezout's theorem. Indeed, this bound of 16 is a tribute to the ingenuity of Lee and Liang [57] who were the first to notice the set of tricks presented above and put to rest a number of erroneous conjectures that had been populating the literature up to that point.…”

Section: Number Of Inverse Kinematics Solutionsmentioning

confidence: 90%

See 1 more Smart Citation

A Mathematical Introduction to Robotic Manipulation

Murray¹,

Sastry²,

Li³

2017

2,680

2,002

View full text Add to dashboard Cite

Section: Number Of Inverse Kinematics Solutionsmentioning

confidence: 90%

“…The procedure has been refined by Roth and Raghavan [96] and Manocha and Canny [64], whose account we follow in this chapter. Manseur and Doty [65] gave an example of a robot with 16 inverse kinematic solutions.…”

Section: Bibliographymentioning

confidence: 99%

A Mathematical Introduction to Robotic Manipulation

Murray¹,

Sastry²,

Li³

2017

2,680

2,002

View full text Add to dashboard Cite

“…These are variations of the example of Manseur and Dory [12] that gives 16 real solutions to the IPP. In fact, Problems 6-9 have this property, and then Problems 10-12 have 8, 4 and 0 real solutions, respectively.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…[11]. Complementing these results, Manseur and Dory [12] have found an example where all 16 solutions are real. Although a 16th degree polynomial reduction of the 6R problem has been established, it does not necessarily follow that the fastest, most numerically stable numerical method for this problem must be based on such a reduction.…”

mentioning

confidence: 75%

See 1 more Smart Citation

Solving the 6R inverse position problem using a generic-case solution methodology

Wampler

Morgan

1991

Mechanism and Machine Theory

View full text Add to dashboard Cite

AlmU'net--This paper considers the computation of all solutions to the inverse position problem for general six-revolute-joint manipulators. Instead of reducing the problem to one highly complicated input-output equation, we work with a system of I I very simple polynomial equations. Although the total degree of the system is large (1024), using the "method of the generic case" we show numerically that the generic number of solutions is 16, in agreement with previous works. Moreover. we present an elEcient nun~rical method for finding all 16 solutions, based on coe~icient-parameter polynomial continuation. We present a set of 41 test problems, on which the algorithm used an average of le-~ than l0 s of CPU time on an IBM 370-3090 in double precision FORTRAN. The methodology applies equally well to other problems in kinematics that can be formulated as polynomial systems.

show abstract

A kinematic view of loop closure

et al. 2004

View full text Add to dashboard Cite

We consider the problem of loop closure, i.e., of finding the ensemble of possible backbone structures of a chain segment of a protein molecule that is geometrically consistent with preceding and following parts of the chain whose structures are given. We reduce this problem of determining the loop conformations of six torsions to finding the real roots of a 16th degree polynomial in one variable, based on the robotics literature on the kinematics of the equivalent rotator linkage in the most general case of oblique rotators. We provide a simple intuitive view and derivation of the polynomial for the case in which each of the three pair of torsional axes has a common point. Our method generalizes previous work on analytical loop closure in that the torsion angles need not be consecutive, and any rigid intervening segments are allowed between the free torsions. Our approach also allows for a small degree of flexibility in the bond angles and the peptide torsion angles; this substantially enlarges the space of solvable configurations as is demonstrated by an application of the method to the modeling of cyclic pentapeptides. We give further applications to two important problems. First, we show that this analytical loop closure algorithm can be efficiently combined with an existing loop-construction algorithm to sample loops longer than three residues. Second, we show that Monte Carlo minimization is made severalfold more efficient by employing the local moves generated by the loop closure algorithm, when applied to the global minimization of an eight-residue loop. Our loop closure algorithm is freely available at http://dillgroup. ucsf.edu/loop_closure/.

show abstract

A Robot Manipulator With 16 Real Inverse Kinematic Solution Sets

Cited by 42 publications

References 6 publications

A Mathematical Introduction to Robotic Manipulation

A Mathematical Introduction to Robotic Manipulation

Solving the 6R inverse position problem using a generic-case solution methodology

A kinematic view of loop closure

Contact Info

Product

Resources

About