Sequential Linear Quadratic Optimal Control for Nonlinear Switched Systems

Abstract

In this contribution, we introduce an efficient method for solving the optimal control problem for an unconstrained nonlinear switched system with an arbitrary cost function. We assume that the sequence of the switching modes are given but the switching time in between consecutive modes remains to be optimized. The proposed method uses a two-stage approach as introduced by Xu and Antsaklis (2004) where the original optimal control problem is transcribed into an equivalent problem parametrized by the switching times and the optimal control policy is obtained based on the solution of a two-point boundary value differential equation. The main contribution of this paper is to use a Sequential Linear Quadratic approach to synthesize the optimal controller instead of solving a boundary value problem. The proposed method is numerically more efficient and scales very well to the high dimensional problems. In order to evaluate its performance, we use two numerical examples as benchmarks to compare against the baseline algorithm. In the third numerical example, we apply the proposed algorithm to the Center of Mass control problem in a quadruped robot locomotion task.

Trajectory Optimization With Implicit Hard Contacts

“…Each phase uses contact-consistent dynamics [8] and/or the corresponding contact constraints [1], [9]- [12]. While this eliminates the hybrid nature of the problem, the sequence of contact configurations (i.e., the gait) must be known a priori.…”

Real-time motion planning of legged robots: A model predictive control approach

“…Here, we have further restricted our switched system model by assuming that the transitions are triggered by predefined switching times, in between predefined sequence of subsystems. For more general treatment of this problem refer to [12], [13].…”

AdaPT: Zero-Shot Adaptive Policy Transfer for Stochastic Dynamical Systems

“…An immediate avenue of future investigation is, therefore, expanding the work presented here to environments with discrete and discontinuous dynamics such as contact. Recently, Farshidian et al [7] have extended an iteratively linearized nonlinear MPC, similar to ours, to switching linear systems, which may have potential as a foundation on which to develop a capable contact formulation of ADAPT. Additionally, recent work has developed robust, receding horizon tube controllers that allow the establishment of explicit tubes in the state space [26].…”