In this study, the main configuration of the robot is a
three-link manipulator mounted on a mobile suspended
platform. Two rear driving wheels and one front caster
wheel support the platform, as shown in Figure 1.
Multi-input shaping technique is applied to reduce the
vibration of a mobile robot when the manipulator is
static. Considering the CG shift, the input shapers evaluating
both robustness and settling time are optimized
by PSO with chaos. The introduced shapers have the
vibration reduction capabilities of the original shapers,
and exhibit improvement in robustness and settling
time. When the manipulator and suspended platform
move simultaneously, the direct path method (DPM) is
introduced (Moosavian and Papadopoulos, 2004) to
model the system considering the dynamics of the
manipulator and the interaction between the platform
and manipulator. Based on cubic splines the time-jerk
synthetic optimal trajectory is described mathematically
by taking account of both the minimum execution
time and the minimax approach of jerks with
kinematics constraints such as the upper bounds of velocity
and acceleration. The optimal trajectory of each
joint is obtained by using PSO with chaos. The residual
vibration can be reduced by forcing the manipulator
along the generated optimal trajectory.
The remainder of this paper is organized as follows:
Section 2 introduces the PSO algorithm and PSO with
chaos. Problems one and two are presented in Sections
3 and 4, respectively, through formulating the mathematical
models, designing the optimization schemes, and
discussing the results. Finally, conclusions are provided
in Section 5.
2. Particle s