On-line Generation of Trajectories Using Singular Spectrum Analysis: A Non-parametric Approach

Abstract

Complex control applications, such as robotics and aerospace engineering, often require nonlinear control strategies. In the backstepping, feedback linearization, and sliding mode control, online trajectory generation is a major requirement in improving the controller performance, leading to high precision tracking. Its purpose is to generate continuous and bounded trajectories that are derivatives of a rough input reference signal, such as steps and pulses. In this context, this paper proposes the use of a non-parametric filter based on the real- time Singular Spectrum Analysis (SSA) method for online trajectory generation. The SSA is highly adaptive to the behavior of signals, including non-stationary ones, through its spectral decomposition. Additionally, is more selective than a simple Finite Impulse Response (FIR) filter, commonly used for generating trajectories. It can identify and extract components, smooth, and denoise a signal. Some experimental results show that SSA can be used as trajectory filter, by successfully generating bounded derivatives from discontinuous input signals. Moreover, empirical adjustment of the fixed filter parameters resulted in similar responses as those obtained for a parametric trajectory filter. These findings provide a potential mechanism for further researches regarding complex and non-stationary signals.