Constrained motion control using vector potential fields

Abstract

This paper discusses the generation of a control signal that would instruct the actuators of a robotics manipulator to drive motion along a safe and well-behaved path to a desired target. The proposed concept of navigation control along with the tools necessary for its construction achieve this goal. The most significant tool is the artificial vector potential field which shows a better ability to steer motion than does a scalar potential field. The synthesis procedure emphasizes flexibility so that the effort needed to modify the control is commensurate with the change in the geometry of the workspace. Theoretical development along with simulation results are provided. Index Terms-Motion planning, nonlinear control, robotics manipulators, vector potential fields. NOMENCLATURE NC Navigation control. PF Potential field. VPF Vector potential field. SPF Scalar potential field. BVP Boundary value problem. VBVP Vector boundary value problem. SBVP Scalar boundary value problem. BEM Boundary element method. LAC Local alignment control. PPC Penetration prevention control. BLAC Boundary local alignment control. BPPC Boundary penetration prevention control.

Harmonic Potential Fields: an Effective Tool for Generating a Self-Organizing Behavior

“…a hybrid, PDE-ODE controller (HPC) to convert the acquired data into in-formation that is encoded in the structure of the micro-control action group. For more details about this type of control see (Masoud & Masoud, 2000a;Masoud & Masoud,1998;Masoud & Masoud, 1997;Masoud & Masoud,1994;Masoud & Masoud, 2000b;Masoud & Masoud, 2002). …”

“…moving out of the way, figure 25) The radial component of the control (ucr i ) may be constructed as: (17) where both the weighting function σ, and the scalar potentials Vr's are positive, spherically symmetric, monotonically decreasing functions whose values are zero for ' ii x-x ≥ρ . As for uct i , it may be constructed as : (18) where ∇⋅ is the divergence operator, and A i is a vector potential field (Masoud & Masoud, 2000b) selected so that:…”

Hyper Redundant Manipulators

“…The control law (57)-(59) modifies the system potential and the Lagrange equation (48)- (50) (Masoud & Masoud, 2000) become…”

Artificial Coordinating Field Based Motion Planning of Mobile Robots

“…It shall be noted that similar but different work to our ACF defined above can be found in literature. Note in Masoud and Masoud (2000), two orthogonal fields were used, a scalar potential field in normal space and a circular field in tangent space around obstacles, to locally switch the robot from one trajectory to another in order to adapt the unknown changing environments. The idea of orthogonal fields is very similar to ours.…”