Feedback Control of a Planar Space Robot Using a Moving Manifold

Applications of Optimal Trajectory Planning and Invariant Manifold Based Control for Robotic Systems in Space

“…If a trajectory of the link angles crosses the zero holonomy curve under the condition of constant radius, as presented in (Hokamoto & Funasako, 2007), virtual goal link angles, which asymptotically reach the goal angles, are set for the link trajectory not to cross the zero holonomy curve. In the second step, the state variables slide along the manifold until they reach the goal states.…”

“…However, their method suffers from a slow rate of convergence if the desired attitude and joint angles are near zero holonomy curves, which are defined as curves in the joint space for which the first-order Lie bracket becomes zero, that is, when the attitude of the main body of a space robot cannot be changed by controlling the joint angles. In order to overcome this disadvantage of the radially isometric orientation based control method, Hokamoto and Funasako (Hokamoto & Funasako, 2007) have proposed a modified version of the smooth time-invariant feedback method by introducing a moving manifold that has a virtual desired point. However, time delay for the planar space robot has apparently not yet been considered.…”

An Adaptive Invariant Manifold-Based Switching Control for a Planar Two-Link Space Robot

“…16), virtual goal link angles, which asymptotically reach the goal angles, are set so that the link trajectory does not cross the zero-holonomy curve.…”

“…In order to overcome this disadvantage of the radially isometric orientation-based control method, Hokamoto and Funasako 16) have proposed a modified version of the smooth time-invariant feedback method by introducing a moving manifold that has a virtual desired point. However, time delay for the planar space robot has apparently not yet been considered.…”

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] No smooth timeinvariant control methods that can stabilize nonholonomic systems exists, even if the system is controllable. This negative fact is well-known as Brockett's theorem.…”