A new approach to solve the kinematics resolution of a redundant robot

Technical Report · Thu Mar 01 04:00:00 EST 1990

OSTI ID:7155137

Belmans, P; Culioli, J C

A classical redundancy resolution scheme for an m-degree of freedom robot involves the numerical or symbolic computation of the Moore-Penrose pseudo-inverse of the Jacobian matrix, which in turn leads to a least norm solution for the joint velocities. Since the Jacobian matrix may be ill-conditioned, the computation of the inverse may often turn out to be lengthy and/or inaccurate. In this paper, we propose an alternative method to find this least norm solution. Namely we modify the original underdetermined problem by transforming it into a set of determined new problems. We compute in parallel the solutions of these problems and find their least norm simplex combination. We prove that if the dimension of the task-space is n, we need only (m {minus} n + 1) such solutions. We also show that the approach can take into account obstacle avoidance and maximum of manipulability or any other type of analytical criterion. We apply the method to a planar redundant arm. 11 refs., 2 figs.

• Research Organization: Oak Ridge National Lab., TN (USA)
• Sponsoring Organization: DOE/ER
• DOE Contract Number: AC05-84OR21400
• OSTI ID: 7155137
• Report Number(s): ORNL/TM-11435; CESAR--89/53; ON: DE90010213
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420200* -- Engineering-- Facilities
Equipment
& Techniques
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ALGORITHMS
DEGREES OF FREEDOM
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
FUNCTIONS
LAGRANGIAN FUNCTION
MATHEMATICAL LOGIC
PARTIAL DIFFERENTIAL EQUATIONS
ROBOTS