dynamic trajectory

In the field of network planning, local optimization techniques are frequently applied to improve the topology of the network by determining between which nodes a connection should exist. In many cases, some links can be merged at extra nodes (Steiner points) in order to save some costs. Finding these extra points belongs to the weighted Fermat-Weber-problem. In this paper, a new representation and construction of the solution to the Fermat-problem is proposed. General conditions of the technological applicability are presented. Furthermore, upper bounds are given to the achievable cost saving in advance without the construction of the Steiner points.

A cable suspended robot can be moved beyond its static workspace while keeping all cables in tension, by relying on end-effector inertia forces. This allows the robot capabilities to be extended by choosing suitable dynamical trajectories. In this paper, we study 3D elliptical motions, which are the most general case of spatial sinusoidal oscillations, for a robot with a point-mass end-effector and an arbitrary base architecture. We find algebraic conditions that define the range of admissible frequencies for feasible trajectories; furthermore, we show that, under certain conditions, a special frequency exists, which allows arbitrarily large oscillations to be reached. We also study transition trajectories that displace the robot from an initial state of rest (within the static workspace) to the elliptical trajectory, and vice versa.

Cable-suspended robots may move beyond their static workspace by keeping all cables under tension, thanks to end-effector inertia forces. This may be used to extend the robot capabilities, by choosing suitable dynamical trajectories. In this paper, we consider three-dimensional (3D) elliptical trajectories of a point-mass end effector suspended by three cables from a base of generic geometry. Elliptical trajectories are the most general type of spatial sinusoidal motions. We find a range of admissible frequencies for which said trajectories are feasible; we also show that there is a special frequency, which allows the robot to have arbitrarily large oscillations. The feasibility of these trajectories is verified via algebraic conditions that can be quickly verified, thus being compatible with real-time applications. By generalizing previous studies, we also study the possibility to change the frequency of oscillation: this allows the velocity at which a given ellipse is tracked to b...

Highlights • A cable-suspended robot is presented with a spatial purely translational motion. • Several special architectures are identified with distinctive and useful features. • The singularity-free/reachable/interference-free workspaces are analytically found. • The theoretical findings are validated by experimental tests. • The robot can perform dynamic trajectories outside the static equilibrium workspace.

A cable suspended robot can be moved beyond its static workspace while keeping all cables in tension, by relying on end-effector inertia forces. This allows the robot capabilities to be extended by choosing suitable dynamical trajectories. In this paper, we study 3D elliptical motions, which are the most general case of spatial sinusoidal oscillations, for a robot with a point-mass end-effector and an arbitrary base architecture. We find algebraic conditions that define the range of admissible frequencies for feasible trajectories; furthermore, we show that, under certain conditions, a special frequency exists, which allows arbitrarily large oscillations to be reached. We also study transition trajectories that displace the robot from an initial state of rest (within the static workspace) to the elliptical trajectory, and vice versa.

Cable-suspended robots may move beyond their static workspace by keeping all cables under tension, thanks to end-effector inertia forces. This may be used to extend the robot capabilities, by choosing suitable dynamical trajectories. In this paper, we consider three-dimensional (3D) elliptical trajectories of a point-mass end effector suspended by three cables from a base of generic geometry. Elliptical trajectories are the most general type of spatial sinusoidal motions. We find a range of admissible frequencies for which said trajectories are feasible; we also show that there is a special frequency, which allows the robot to have arbitrarily large oscillations. The feasibility of these trajectories is verified via algebraic conditions that can be quickly verified, thus being compatible with real-time applications. By generalizing previous studies, we also study the possibility to change the frequency of oscillation: this allows the velocity at which a given ellipse is tracked to b...

In this paper, we have presented the 3D cables parallel robot in pyramid’s form. The dynamic equation has been established including the dynamic behavior, in this context; we investigated to use the Runge Kutta method of 4th order to solving non-linear partial differential equation of our system. The main contribution of this work is firstly: a graphical user interface (GUI) has been developed and implemented based on the geometric model, in order to visualizing the position of end effect or, taking account model uncertainties and payload variation. Secondly, we have studied and solved our system’s dynamical equation with implementation the PD control. This last, applied for different trajectories so as to test the accurate tracking the desired trajectory simulation using MATLAB software. As a result, the simulation tests on this robot verify the efficiency performance of the proposed controller.

The paper investigates the motion planning of a suspended service robot platform equipped with ducted fan actuators. The platform consists of an RRT robot and a cable suspended swinging actuator with ducted fans that form a subsequent parallel kinematic chain. The system is redundant and, in spite of the complementary ducted fan actuators, it is underactuated. The paper discusses the inverse dynamics problem and proposes trajectory generation methods for the motion planning of the complex hybrid robotic system. The closed form results include the desired actuator forces as well as the nominal swing angle corresponding to the desired motion of the carried payload. Numerical simulation and experiments demonstrate the applicability of the presented concepts.

This paper studies the kinematics and statics of cable-driven parallel robots with less than six cables, in crane configuration. A geometrico-static model is provided, together with a general procedure aimed at efficiently solving, in analytical form, the inverse and direct position problems. The stability of equilibrium is assessed within the framework of a constrained optimization problem, for which a purely algebraic formulation is provided. A spatial robot with three cables is studied as an application example.

This paper presents an efficient interval-analysis-based algorithm to solve the direct geometrico-static problem (DGP) of underconstrained cable-driven parallel robots (CDPRs). Solving the DGP for a generic CDPR consists of finding all possible equilibrium poses of the end effector for the given cable lengths. Since cables impose unilateral constraints, configurations with one or more slack cables may occur. When the number of taut cables is smaller than six the robot is underconstrained and the DGP solutions must be found considering loop-closure and mechanical equilibrium equations simultaneously. The presented algorithm can find all DGP solutions of a generic CDPR in a numerically robust and safe way. By using interval analysis the proposed procedure can directly search for real solutions with non-negative cable tensions and it can take advantage of the physical constraints of the robot. The implemented procedure is discussed in detail, and the testing and experimental validation...

We consider dynamic motions of a spatial robot suspended by six cables, arranged so as to form three parallelograms. Each parallelogram is composed by two parallel cables sharing the same length. Due to this arrangement, the end-effector can only translate. The cables in each parallelogram can be actuated by one motor: only three motors are then required, which reduces the robot complexity and cost. This robot may perform pick-and-place operations over large workspaces. We find tight conditions for feasibility of dynamic trajectories for the general architecture, and also special conditions such that the robot is dynamically equivalent to a 3-cable robot with a point-mass end-effector: then, the feasibility conditions previously developed for the dynamic trajectories of 3-cable point-mass robots can be profitably reused for the present case. To practically realize such dynamic trajectories, we also analyze the reachable, singularity-free and interference-free workspace, finding analytical expressions of their loci. Finally, we perform experiments where the robot follows dynamic trajectories outside its static workspace, thus finding confirmation that the orientation remains approximately constant.

Cable suspended robots may move beyond their static workspace by keeping all cables under tension, thanks to end-effector inertia forces. This may be used to extend the robot capabilities, by choosing suitable dynamical trajectories. In this paper, we consider 3D elliptical trajectories of a point-mass end-effector suspended by 3 cables from a base of generic geometry. Elliptical trajectories are the most general type of spatial sinusoidal motions. We find a range of admissible frequencies for which said trajectories are feasible; we also show that there is a special frequency which allows the robot to have arbitrarily large oscillations. The feasibility of these trajectories is verified via algebraic conditions that can be quickly verified, thus being compatible with real-time applications. By generalizing previous studies, we also study the possibility to change the frequency of oscillation: this allows the velocity at which a given ellipse is tracked to be varied, thus providing more latitude in the trajectory definition. We finally study transition trajectories to move the robot from an initial state of rest (within the static workspace) to the elliptical trajectory (and vice versa) or to connect two identical ellipses having different centres.

We present in this paper a new mechanical architecture for a parallel manipulator. We address the problem of the determination of the singular configurations of this architecture. Then we show that the direct kinematic problem has at most 16 solutions and exhibit an algorithm to find all the solutions.

This paper presents an efficient interval-analysis-based algorithm to solve the direct geometrico-static problem (DGP) of underconstrained cable-driven parallel robots (CDPRs). Solving the DGP for a generic CDPR consists of finding all possible equilibrium poses of the end effector for the given cable lengths. Since cables impose unilateral constraints, configurations with one or more slack cables may occur. When the number of taut cables is smaller than six the robot is underconstrained and the DGP solutions must be found considering loop-closure and mechanical equilibrium equations simultaneously. The presented algorithm can find all DGP solutions of a generic CDPR in a numerically robust and safe way. By using interval analysis the proposed procedure can directly search for real solutions with non-negative cable tensions and it can take advantage of the physical constraints of the robot. The implemented procedure is discussed in detail, and the testing and experimental validation on working prototypes are presented.

Abstract This paper studies under-constrained cable-driven parallel robots with three cables. A major challenge in the study of these manipulators is the intrinsic coupling between kinematics and statics, which must be tackled simultaneously. In this contribution, a general elimination procedure is provided that solves the direct geometrico-static problem, which consists in determining the platform posture and the cable tensions when the cable lengths are assigned. The problem is proven to have up to 156 complex solutions.

This paper presents the inverse geometrico-static analysis of under-constrained cable-driven parallel robots with 4 cables.
The problem consists in finding all equilibrium configurations of the end-effector when either its orientation or the center-of-mass's position is assigned.
In both cases, a further point of the end-effector is constrained to lie on a given plane.
A major challenge is posed by the intrinsic coupling between kinematics and statics, which must be tackled simultaneously.
The problems at hand are solved by analytical elimination procedures, thus leading to univariate polynomials free of spurious factors.
All potential solutions may be real.