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This paper presents an effective method for planning and optimizing robot motions in joint space using via-points. The via-point formulation allows for a sparse movement representation which is inherently smooth according to a minimum jerk criterion. In this research we focus on two aspects. First, we present an initialization method to find a feasible number of via-points and their distribution in...
To enable safe and efficient human-robot collaboration in shared workspaces, it is important for the robot to predict how a human will move when performing a task. While predicting human motion for tasks not known a priori is very challenging, we argue that single-arm reaching motions for known tasks in collaborative settings (which are especially relevant for manufacturing) are indeed predictable...
This paper proposes a method called Segmentation-adaptive Pseudospectral collocation to address the problem of safe trajectory generation in missions with cooperating multiple aerial vehicles. Pseudospectral collocation can generate optimized collision-free trajectories, but for multiple aerial vehicles it cannot guarantee that the safety separation distance is maintained in the whole trajectories,...
Model predictive control is a well established strategy for dealing with saturating actuator problems. The essential feature of the method is a receding horizon quadratic optimal control problem which is solved subject to input constraints. On the other hand, anti-windup methods are ad-hoc procedures which achieve input saturation in an instantaneous fashion. Both methods are known to perform well...
This paper presents the solution of an optimal control problem for hybrid dynamical systems. A general method using Lagrange multipliers is applied to a class of such systems. A trajectory pursuit problem is solved by means of steepest descent methods. Numerical examples involving hysteresis phenomena are given.
In this article it is investigated how, alternative to e.g. the standard pulse or blocking mechanisms, other input parametrizations can be used in model predictive control to improve the trade-off between performance and complexity. An efficient parametrization is obtained using the observation that the class of all solutions to a finite or infinite horizon LQ control problem can be parametrized with...
This paper aims at providing some new insights into the linear quadratic optimization problem in the behavioral approach. A new problem statement is given and some comparisons with the standard LQ problem in the state space approach are provided. The problem solution is analyzed in detailed terms so that all optimal trajectories can be easily computed from the initial data. Noteworthy, the set of...
Periodic deformations of organs which are due to respiratory movements may be critical disturbances for surgeons manipulating robotic control systems during laparoscopic interventions or tele-surgery. Indeed, the surgeon has to manually compensate for these motions if accurate gestures are needed, like, e.g., during suturing. This paper proposes a repetitive model predictive control scheme for driving...
Quantification of spin density, R∗2 decay and off-resonance frequency maps is very important in some applications of magnetic resonance imaging (MRI). To reconstruct these parameter maps, a time-varying model such as mono-exponentials must be used to represent the signal from each voxel. When only a single-shot trajectory is adopted, the underlying reconstruction problem is significantly nonlinear...
In a previous work, we showed how the flatness of the heat equation with two controls at both ends of the domain could be used to generate solutions to create solutions to Burgers' equation. The created solutions were thought as a motion planner for a multi-agent systems of e.g. ground robots, UAVs. The trajectories of the different particles of the PDE are to be used as input for a feed-forward control...
This paper demonstrates a method for finding the cost function and state observer to be used in model predictive control (MPC) so that when constraints are inactive a pre-existing low order controller is reproduced. The MPC controller thereby inherits its desirable properties. This can be used as a baseline for further tuning. The available degrees of design freedom are explored, in order to facilitate,...
New problems of optimal path coordination for multiple vehicles are introduced, formulated and solved in the framework of dynamic optimization. The novelty of these problems arises in several ways. The cost function and the dynamics include non-trivial dependencies, modeled through existential quantification over groups of vehicles - this leads to non-Lipschitz behavior and to non-standard optimal...
A communication-based distributed model predictive control scheme for a set of dynamically decoupled autonomous systems (agents) is proposed. The individual dynamics are described by discrete-time linear systems. Locally, each agent obeys a model predictive controller which minimizes a given local cost-function. Coupling between the agents occurs only through state-constraints. It is assumed that...
New first-order necessary conditions of optimality for control problems with state constraints are provided. These conditions are a variant of the nonsmooth maximum principle in which an Euler-Lagrange inclusion is involved. The main novelty of the result is precisely the ability to address state constraints, generalizing a known Euler-Lagrange inclusion for optimal control problems. The conditions...
Event-triggered control and self-triggered control are an important control strategy in networked control systems. Event-triggered control is a control method that determines transmissions of the control input and the measured signal depending on measurement information. Self-triggered control is a control method that the control input and the (non-uniform) sampling interval are computed simultaneously...
This paper presents an algorithm for trajectory planning of dual-stage positioning systems based on a simplified model predictive control approach. Compared to other methods available in literature, the proposed solution has the advantage of generating the feasible trajectories by explicitly taking into account the kinematic constraints of each actuator. This guarantees that the actuators' limits...
Path planning is an interesting topic which is affected by lots of variables, as: time, energy, torque and stability. In this study, a new method based on Big Bang-Big Crunch algorithm is proposed to find optimum values of the parameters of a path and a cost function in order to minimize applied torque and tracking error. For this purpose the mathematical model of the manipulator is derived with mainly...
This paper discusses a motion planning method for assembling a ring-shaped elastic part to a cylindrical part by using a dual-arm manipulator. When assembling a ring-shaped elastic part, it is important to keep the amount of elastic deformation as small as possible during the assembly task. To achieve this purpose, we show that it is effective to utilize the Covariant Hamiltonian Optimization and...
We present algorithms for inferring the cost function and reference trajectory from human demonstrations of hand-writing tasks. These two key elements are then used, through optimal control, to generate an impedance-based controller for a robotic hand. The key novelty lies in the flexibility of the feature design in the composition of the cost function, in contrast to the traditional approaches that...
In this paper, we address the problem of seeking a source that emits signal described by a function that is radially symmetric, and decays with increasing distance in a complex environment with obstacles. Electromagnetic signals, acoustic signals, vapor emission, etc, are examples of such signals. In contradistinction to existing techniques, we use a non-gradient based technique known as Particle...
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