Fast design of the QP-based optimal trajectory for the Eclipse-11 motion simulator

The main difficulty in realizing a motion simulator comes from the constraints on its workspace. The so-called washout filter prevents the simulator from being driven to go off its pre-determined boundaries and generate excessive torques, while it possible for the motion simulator to realize the real-world motion with high fidelity. The proposed approach in this paper formulates the task of designing a washout filter as a quadratic programming (QP) with inequality constraints. Although efficient in solving problem of relatively small size, the direct approach to the solution of the QP often results in computational burdens that reach beyond the capacity of modern computing power, which amounts to O(N³) flops and O(N²) storage space (W = 10⁴∼10⁵, typically). By judiciously exploiting the Toeplitz structures of the underlying matrices, an orders-of-magnitude faster algorithm is obtained to reduce the computational burdens to O(N log₂ N) flops and O(N) storage space.