An Offline-Sampling SMPC Framework With Application to Autonomous Space Maneuvers

Abstract

In this paper, a sampling-based Stochastic Model Predictive Control algorithm is proposed for discrete-time linear systems subject to both parametric uncertainties and additive disturbances. One of the main drivers for the development of the proposed control strategy is the need of reliable and robust guidance and control strategies for automated rendezvous and proximity operations between spacecraft. To this end, the proposed control algorithm is validated on a floating spacecraft experimental testbed, proving that this solution is effectively implementable in real-time. Parametric uncertainties due to the mass variations during operations, linearization errors, and disturbances due to external space environment are simultaneously considered.The approach enables to suitably tighten the constraints to guarantee robust recursive feasibility when bounds on the uncertain variables are provided. Moreover, the offline sampling approach in the control design phase shifts all the intensive computations to the offline phase, thus greatly reducing the online computational cost, which usually constitutes the main limit for the adoption of Stochastic Model Predictive Control schemes, especially for low-cost on-board hardware. Numerical simulations and experiments show that the approach provides probabilistic guarantees on the success of the mission, even in rather uncertain and noise situations, while improving the spacecraft performance in terms of fuel consumption.

Sample-Based SMPC for Tracking Control of Fixed-Wing UAV

“…The above linear constraints constitute a probabilistically guaranteed approximation of the actual constraint observed online. In particular, it was shown in [23] that if, for given probabilistic parameters α , β , γ ∈ (0, 0.14), and δ ∈ (0, 1), the samples are drawn such that N x ≥Ñ (n + m, , δ), N u ≥Ñ (n + m, β , δ), N T ≥Ñ (n + T m, γ , δ), withÑ (·, ·, ·) given in [16]. The linear constraints (12), (13), (14), possibly after constraint reduction, can be summarized in the following linear constraint set…”

“…Motivated by the considerations above, the paper develops a framework for FW-UAVs guidance and control, the combination of which can reduce the time of flight and optimize the monitoring of the selected area. The proposed approach successfully applies in a real-time framework recent theoretical results obtained by the research team involved in the project: a guidance scheme developed in [14], and an offline sample based SMPC approach developed in [15], [16]. The use of this latter is important for several reasons: (i) the scheme guarantees probabilistic robust satisfaction of the imposed constraints, at a lower computational cost, and (ii) it is shown that such approach is feasible for medium-high sampling frequencies involved in the application.…”

“…The use of this latter is important for several reasons: (i) the scheme guarantees probabilistic robust satisfaction of the imposed constraints, at a lower computational cost, and (ii) it is shown that such approach is feasible for medium-high sampling frequencies involved in the application. As briefly said before, the effectiveness of the approach for real-time implementation has been validated for a space application on an experimental testbed, as described in [16]. In the application here chosen, the goal is more challenging due to the much faster dynamics characterizing the UAV dynamics with respect the spacecraft dynamics, including atmospheric disturbances (i.e.…”

“…Before running the online control algorithm: 1) Compute matrixS; draw uncertainty and noise samples and construct sets D and D R in(16). ONLINE IMPLEMENTATION.…”

Design and validation of an MPC controller for CMG-based testbed

“…As clear from literature (Wang and Boyd 2009;Mayne 2014;Mammarella et al 2018), however, one of the main drawback of the MPC control scheme is related to the online optimization problem and to the difficulty of embedding a real-time solver for the on-board implementation. A practical solution, usually used for MPC implementation on embedded systems, is the offline evaluation of the control law, uploaded on-board by means of lookup tables Bemporad et al (2002).…”