Abstract
Kinematics and its control application are presented for a Stewart platform whose base plate is installed on a floor in a moving ship or a vehicle. With a manipulator or a sensitive equipment mounted on the top plate, a Stewart platform is utilized to mitigate the undesirable motion of its base plate by controlling actuated translational joints on six legs. To reveal closed loops, a directed graph is utilized to express the joint connections. Then, kinematics begins by attaching an orthonormal coordinate system to each body at its center of mass and to each joint to define moving coordinate frames. Using the moving frames, each body in the configuration space is represented by an inertial position vector of its center of mass in the three-dimensional vector space ℝ3, and a rotation matrix of the body-attached coordinate axes. The set of differentiable rotation matrices forms a Lie group: the special orthogonal group, SO(3). The connections of body-attached moving frames are mathematically expressed by using frame connection matrices, which belong to another Lie group: the special Euclidean group, SE(3). The employment of SO(3) and SE(3) facilitates effective matrix computations of velocities of body-attached coordinate frames. Loop closure constrains are expressed in matrix form and solved analytically for inverse kinematics. Finally, experimental results of an inverse kinematics control are presented for a scale model of a base-moving Stewart platform. Dynamics and a control application of inverse dynamics are presented in the part II-paper.
Highlights
When manipulators, which require precise positioning, operate in moving vehicles or ships, it becomes economical to utilize a Stewart platform [1], whose sole role is to stabilize the orientation and the translation of its top table onto which the manipulators are attached
Fixed-base Stewart platforms have been popularly utilized in flight simulators, vehicle driving simulators, trajectory tracking apparatus, and immersed virtual-reality theaters in amusement parks
To commence kinematics using moving frames, the configuration space is defined along the generic closed loop in Fig. 2b by attaching orthonormal coordinate systems at the centers of mass of constituent bodies as well as at the joints
Summary
Facilitates effective matrix computations of velocities of body-attached coordinate frames. Loop closure constrains are expressed in matrix form and solved analytically for inverse kinematics. Experimental results of an inverse kinematics control are presented for a scale model of a base-moving Stewart platform. Dynamics and a control application of inverse dynamics are presented in the part II-paper. Keywords Base-moving Stewart platform Inverse kinematics control Lie group Motion compensation Moving frame method
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