Kinematic Control of Redundant Manipulators: Generalizing the Task-Priority Framework to Inequality Task

Redundant mechanical systems like humanoid robots are designed to fulfill multiple tasks at a time. A task, in velocity-resolved inverse kinematics, is a desired value for a function of the robot configuration that can be regulated with an ordinary differential equation (ODE). When facing simultaneo...

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Bibliographic Details
Published in:IEEE transactions on robotics Vol. 27; no. 4; pp. 785 - 792
Main Authors: Kanoun, O., Lamiraux, F., Wieber, P-B
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.08.2011
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Applied sciences
Computer science; control theory; systems
Control
Control theory. Systems
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
hierarchy
Humanoid
humanoid robot
Humanoid robots
Inequalities
inequality constraints
inverse kinematics
Joints
Kinematics
Linear matrix inequalities
Manipulators
Mathematical analysis
Ordinary differential equations
Physics
Priorities
Quadratic programming
redundancy
Redundant
Robotics
Robots
Silicon
Solid dynamics (ballistics, collision, multibody system, stabilization...)
Solid mechanics
task priority
Tasks
Redundant system
inequality constraints
Differential equation
Redundancy
Least squares problem
hierarchy
Solid dynamic
Constraint satisfaction
inverse kinematics
task priority
Robotics
Hierarchized structure
Manipulator
Inverse problem
Humanoid robot
Control
Kinematics
Inequality constraint
Equality constraint
Mechanical system
ISSN:1552-3098, 1941-0468
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Summary:Redundant mechanical systems like humanoid robots are designed to fulfill multiple tasks at a time. A task, in velocity-resolved inverse kinematics, is a desired value for a function of the robot configuration that can be regulated with an ordinary differential equation (ODE). When facing simultaneous tasks, the corresponding equations can be grouped in a single system or, better, sorted in priority and solved each in the solutions set of higher priority tasks. This elegant framework for hierarchical task regulation has been implemented as a sequence of least-squares problems. Its limitation lies in the handling of inequality constraints, which are usually transformed into more restrictive equality constraints through potential fields. In this paper, we propose a new prioritized task-regulation framework based on a sequence of quadratic programs (QP) that removes the limitation. At the basis of the proposed algorithm, there is a study of the optimal sets resulting from the sequence of QPs. The algorithm is implemented and illustrated in simulation on the humanoid robot HRP-2.
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ISSN:1552-3098
1941-0468
DOI:10.1109/TRO.2011.2142450