Fast nonlinear Model Predictive Control for unified trajectory optimization and tracking

Abstract

This paper presents a framework for real-time, full-state feedback, unconstrained, nonlinear model predictive control that combines trajectory optimization and tracking control in a single, unified approach. The proposed method uses an iterative optimal control algorithm, namely Sequential Linear Quadratic (SLQ), in a Model Predictive Control (MPC) setting to solve the underlying nonlinear control problem and simultaneously derive the optimal feedforward and feedback terms. Our customized solver can generate trajectories of multiple seconds within only a few milliseconds. The performance of the approach is validated on two different hardware platforms, an AscTec Firefly hexacopter and the ball balancing robot Rezero. In contrast to similar approaches, we perform experiments that require leveraging the full system dynamics.

Experience-driven Predictive Control with Robust Constraint Satisfaction under Time-Varying State Uncertainty

“…That is, we require the ability to compute predictive control commands at sufficiently high rates to ensure stability of these agile systems. Fast MPC solution strategies can be divided into four categories: leveraging fast online optimization techniques [26], optimizing approximate formulations [15], explicit enumeration of equivalent controllers [2], and semi-explicit approaches [7,8,28]. In this work, we consider this last class of techniques due to the reduced reliance on online optimization in a critical control loop and their scalability to available computational resources [28].…”

A Hybrid Method for Online Trajectory Planning of Mobile Robots in Cluttered Environments

“…Moreover, notice that by Theorem 3 the posed QP formulation is feasible. This approach, unlike [11]- [13], [24], avoids iterative formulations.…”

A projection approach to equality constrained iterative linear quadratic optimal control

“…By means of a projection, we limit the set of admissible control inputs δu n at time index n to such controls which • lead to a satisfaction of the linearized state-input constraints immediately and • lead to satisfaction of the linearized pure state constraints at the next upcoming timestep. Hence, we rewrite the pure state constraint in terms of a 'previewed' state-input constraint Dn Nn δx n + En Mn δu n = en dn+1 (13) and at time index n, the control input is to be selected such that it complies with Equation (13), while also minimizing the cost function (6). To achieve both, we propose the following structure for the control update δu n δu n = δu 0 n + P n N En Mn ·ū n…”