Search

In this article, we discuss a sequential algorithm for the computation of a minimum-time speed profile over a given path, under velocity, acceleration, and jerk constraints. Such a problem arises in industrial contexts, such as automated warehouses, where LGVs need to perform assigned tasks as fast as possible in order to increase productivity. It can be reformulated as an optimization problem with a convex objective function, linear velocity and acceleration constraints, and nonconvex jerk constraints, which, thus, represent the main source of the difficulty. While existing nonlinear programming (NLP) solvers can be employed for the solution of this problem, it turns out that the performance and robustness of such solvers can be enhanced by the sequential line-search algorithm proposed in this article. At each iteration, a feasible direction, with respect to the current feasible solution, is computed, and a step along such direction is taken in order to compute the next iterate. The computation of the feasible direction is based on the solution of a linearized version of the problem, and the solution of the linearized problem, through an approach that strongly exploits its special structure, represents the main contribution of this work. The efficiency of the proposed approach with respect to existing NLP solvers is proven through different computational experiments. Note to Practitioners—This article was motivated by the needs of LGV manufacturers. In particular, it presents an algorithm for computing the minimum-time speed law for an LGV along a preassigned path, respecting assigned velocity, acceleration, and jerk constraints. The solution algorithm should be: 1) fast, since speed planning is made continuously throughout the workday, not only when an LGV receives a new task but also during the execution of the task itself, since conditions may change, e.g., if the LGV has to be halted for security reasons and 2) reliable, i.e., it should return solutions of high quality, because a better speed profile allows to save time and even small percentage improvements, say a 5% improvement, has a considerable impact on the productivity of the warehouse, and, thus, determines a significant economic gain. The algorithm that we propose meets these two requirements, and we believe that it can be a useful tool for LGV manufacturers and users. It is obvious that the proposed method also applies to the speed planning problem for vehicles other than LGVs, e.g., road vehicles. [ABSTRACT FROM AUTHOR]

In this paper, we consider the speed planning problem for a robotic manipulator. In particular, we present an algorithm for finding the time-optimal speed law along an assigned path that satisfies velocity and acceleration constraints and respects the maximum forces and torques allowed by the actuators. The addressed optimization problem is a finite-dimensional reformulation of the continuous-time speed optimization problem, obtained by discretizing the speed profile with $n$ points. The proposed algorithm has linear complexity with respect to $n$ and to the number of degrees of freedom. Such complexity is the best possible for this problem. Numerical tests show that the proposed algorithm is significantly faster than algorithms already existing in literature. [ABSTRACT FROM AUTHOR]

Consider a multi-tone multi-user communication system with \mathbf K interfering users and \mathbf N available tones. An effective approach to mitigate interference is through power control at transmitters. In this paper, we consider optimal power allocation to maximize a system utility function, and show that for the two tone cases ( \mathbf N=2 ) with min-rate, harmonic mean, and geometric mean utility functions, the corresponding optimal power allocation problem is NP-hard. This result fills an important gap in the existing literature, which settled the complexity status of different cases involving various utility functions and values of \mathbf N . Our proof is through a reduction from the partitioning problem for the min-rate utility function, and from the independent set problem for the harmonic mean and geometric mean utility functions. [ABSTRACT FROM PUBLISHER]

Trajectories in the operational space could easily cause feasibility issues when they incur in kinematic singularities. In proximity of singular configurations, as known, joint velocities and accelerations could indeed assume unfeasible values, thus worsening the tracking performances of controllers: in case of strong violations of the assigned bounds, manipulators could even be stopped in order to prevent control losses. Problems are especially evident when trajectories are online defined for nonrepetitive tasks. This paper proposes an algorithm for the real-time handling of wrist singularities for nonredundant manipulators. The proposed method makes it possible to execute otherwise unfeasible trajectories by simultaneously preserving an accurate path tracking, by guaranteeing the fulfillment of the assigned longitudinal time law and by fulfilling a given set of bounds on the joint velocities and accelerations. This result is achieved by acting on the orientation of the end-effector: only minor changes are admitted in order to minimize their impact on the process quality. The proposed method has been verified by means of simulations and real experiments. Comparisons have been made with the performances of an analogous commercial system. [ABSTRACT FROM PUBLISHER]

In this paper, we define a discrete dynamical system that governs the evolution of a population of agents. From the dynamical system, a variant of differential evolution (DE) is derived. It is then demonstrated that, under some assumptions on the differential mutation strategy and on the local structure of the objective function, the proposed dynamical system has fixed points toward which it converges with probability one for an infinite number of generations. This property is used to derive an algorithm that performs better than standard DE on some space trajectory optimization problems. The novel algorithm is then extended with a guided restart procedure that further increases the performance, reducing the probability of stagnation in deceptive local minima. [ABSTRACT FROM AUTHOR]