We employ the proximal averaged Newton-type method for optimal control (PANOC) to solve obstacle avoidance problems in real time. We introduce a novel modeling framework for obstacle avoidance which allows us to easily account for generic, possibly nonconvex, obstacles involving polytopes, ellipsoids, semialgebraic sets and generic sets described by a set of nonlinear inequalities. PANOC is particularly well-suited for embedded applications as it involves simple steps, its implementation comes with a low memory footprint and its fast convergence meets the tight runtime requirements of fast dynamical systems one encounters in modern mechatronics and robotics. The proposed obstacle avoidance scheme is tested on a lab-scale autonomous vehicle.
Abstract-This work presents an online distributed motion planning strategy for cooperating vehicles. The motion planning is formulated as an optimization problem that returns smooth trajectories. These are parameterized as splines, which allows a representation with a limited number of variables and enables guaranteed constraint satisfaction with a finite set of constraints. The computations for solving the problem are distributed among the agents by using the Alternating Direction Method of Multipliers (ADMM). In order to cope with a dynamic environment and disturbances, the algorithm is formulated in a receding horizon fashion, such that the future part of a motion trajectory is reoptimized iteratively. The required update time and the amount of inter-agent communication are reduced by performing only one ADMM iteration per update. In this way the method converges over the subsequent path updates. Simulations with a formation of holonomic vehicles in a dynamic environment demonstrate the capability of the proposed approach to generate optimal trajectories at an update rate of 20 Hz.
A methodology is proposed for the design of robust structurally constrained controllers for linear time-delay systems, focusing on decentralised and overlapping fixed-order controllers for Multiple Input Multiple Output (MIMO) systems. The methodology is grounded in a direct optimisation approach and relies on the minimisation of the spectral abscissa and H∞ cost functions, as a function of the controller or design parameters. First, an approach applicable to generic MIMO time-delay systems is presented, which is based on imposing a suitable sparsity pattern with the possibility of fixing elements in the controller parameterisation. Second, we show that if the delay system to be controlled has by itself the structure of a network of coupled identical subsystems, this structure can then be exploited by an improved algorithm for the design of decentralised (or overlapping) fixed-order controllers for the infinite-dimensional system, thereby increasing the computational efficiency and scalability with the number of subsystems. The two approaches, which have been implemented in a publicly available software, support system models in terms of delay differential algebraic equations. They allow to model interconnected systems in a systematic way, and include retarded and neutral systems with delays in state, inputs and outputs. Several numerical examples illustrate the effectiveness of the methodology, as well as its extension towards consensus type problems.
This paper presents a real-time implementation of the proximal gradient method (PGM) in a model predictive control (MPC) setting. In each control update only one iteration of the PGM is performed, while a next update is warm-started using the solution of the previous one. When applied to linear time-invariant (LTI) systems with simple input constraints, the resulting control law becomes extremely simple and offers possibilities to obtain fast control rates even on resourceconstrained hardware. The paper provides a proof of closedloop stability of the real-time PGM applied to LTI systems. A numerical simulation example validates the resulting closedloop performance.
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