This article studies the trajectory planning for underactuated cable-driven parallel robots (CDPRs) in the case of rest-to-rest motions, when both the motion time and the path geometry are ...prescribed. For underactuated manipulators, it is possible to prescribe a control law only for a subset of the generalized coordinates of the system. However, if an arbitrary trajectory is prescribed for a suitable subset of these coordinates, the constraint deficiency on the end-effector leads to the impossibility of bringing the system at rest in a prescribed time. In addition, the behavior of the system may not be stable, that is, unbounded oscillatory motions of the end-effector may arise. In this article, we propose a novel trajectory-planning technique that allows the end effector to track a constrained geometric path in a specified time, and allows it to transition between stable static poses. The design of such a motion is based on the solution of a boundary value problem, aimed at a finding solution to the differential equations of motion with constraints on position and velocity at start and end times. To prove the effectiveness of such a method, the trajectory planning of a six-degrees-of-freedom spatial CDPR suspended by three cables is investigated. Trajectories of a reference point on the moving platform are designed so as to ensure that the assigned path is tracked accurately, and the system is brought to a static condition in a prescribed time. Experimental validation is presented and discussed.
This paper proposes a dynamic trajectory planning method for point-to-point motion of three-degree-of-freedom (three-DOF) cable-suspended parallel robots. Natural frequencies as well as associated ...periodic trajectories that can be obtained from the integration of the dynamic model of an equivalent passive mechanical system are used to design point-to-point trajectories. The trajectories can be used to connect consecutive points in sequence that may lie beyond the static workspace of the robot. The technique ensures zero velocity at each of the target points and continuity of the accelerations. Based on the cable tension constraints, attainable regions can be determined to search for the next target point, while feasible regions of intermediate points are generated in cases for which a given point cannot be directly attained. An example trajectory is performed to illustrate the approach. An experimental implementation is also presented using a three-DOF prototype, and video extensions are provided to demonstrate the results.
Robotic manipulators are becoming increasingly complex systems in order to meet market demands for their safer and more flexible use. Complex robotic systems are modifying the way robots are ...perceived and exploited in several areas. The effectiveness of these systems is challenged by new problems regarding their design, control, and planning, among others. This Special Issue explores recent advances in the dynamics and control of robot manipulators, spanning from linkages to non-conventional serial and parallel robots.
Redundancy resolution of redundantly actuated cable-driven parallel robots (CDPRs) requires the computation of feasible and continuous cable tension distributions along a trajectory. This paper ...focuses on n-DOF CDPRs driven by n + 2 cables, since, for n = 6, these redundantly actuated CDPRs are relevant in many applications. The set of feasible cable tensions of n-DOF (n + 2)-cable CDPRs is a 2-D convex polygon. An algorithm that determines the vertices of this polygon in a clockwise or counterclockwise order is first introduced. This algorithm is efficient and can deal with infeasibility. It is then pointed out that straightforward modifications of this algorithm allow the determination of various (optimal) cable tension distributions. A self-contained and versatile tension distribution algorithm is thereby obtained. Moreover, the worst-case maximum number of iterations of this algorithm is established. Based on this result, its computational cost is analyzed in detail, showing that the algorithm is efficient and real-time compatible even in the worst case. Finally, experiments on two six-degree-of-freedom eight-cable CDPR prototypes are reported.
The maximum cable tension is a crucial parameter in the design of a cable-driven parallel robot (CDPR) since the various mechanical components of the CDPR must be designed to safely withstand the ...loads induced by this maximum tension. For CDPRs having a number of cables at least equal to its number of degree of freedoms (DOFs), this article deals with the determination of the smallest maximum cable tension vectors allowing a required wrench set to be feasible. The problem is formulated as the minimization of the maximum cable tension infinity norm under linear inequality constraints, which include the wrench-feasibility constraints. The solution to this minimization problem is not unique, and the solution set is shown to be a convex polytope in the maximum tension space. Hence, various smallest maximum tension vectors generally exist and the computations of two different solution vectors are introduced. The first vector has all its components equal to the minimum infinity norm, which can be directly obtained from the minimization problem inequality constraints. An algorithm is proposed to determine the second vector as the solution vector having the least possible value for each of its components. The computation of the smallest maximum tension vectors for general required wrench sets are then presented. The cases of particular wrench set definitions relevant to heavy payload manipulation applications are also introduced. Finally, these contributions are applied to the configuration (geometry) optimization of a large-dimension 6-DOF CDPR installed on a building facade to manipulate heavy payloads.
There is a growing interest on the study of continuum parallel robots (CPRs) due to their higher stiffness and better dynamics capacities than serial continuum robots (SCRs). Several works have ...focused on the computation of their geometrico- and kinemato-static models that can be sorted into two main categories. Models based on the continuous Cosserat equations are very accurate but assessing elastic stability with them is tricky, and discretized models allow easily checking the elastic stability, but they require a large number of elastic variables to be accurate. In this article, we extend an approach based on assumed strain modes developed for the dynamics of SCRs to the statics of CPRs. This method is able to predict the robot configuration with an excellent accuracy with a very limited number of elastic variables, contrary to other discretization methods. The method is also more than 100 times faster than finite differences for a better prediction accuracy. Finally, it is possible to assess the robot elastic stability by only checking the Hessian of the potential energy as for any discretization method, thus making the analysis of this property simpler than for the continuous Cosserat model. All results are validated through simulations on two case studies.
Research on continuum parallel robots has been essentially devoted to the computation of their geometricostatic models and of their performance in terms of workspace size, accuracy, compliance, force ...transmission, and manipulability. Their singularity analysis has been limited to the identification of a limited number of singular configurations, without any deep investigation of the physical phenomena occurring in these singularities. In this article, we define the singularity conditions for continuum parallel robots. We provide a straightforward interpretation of the phenomena occurring in singularities. Especially, we prove that some singularities appear when the robot potential energy has a local isovalue. Because of this property, we show that these singularities separate the stable configurations from the unstable ones in the workspace. Moreover, on such singularities, the robot can freely move along a given direction without any constraint under the action of small perturbations. We illustrate the singularity phenomena and their effects by simulations performed with two different continuum parallel robots.
The Fin-Ray principle, inspired by the physiology of fish rays, represents the foundation of a large number of robotic devices. However, despite their popularity, there is not any ad-hoc theoretical ...model technique for the analysis of this family of fingers. This lack is the main motivation of the presented work, which provides the mathematical modeling, analysis, and prototyping of a closed-chain Fin-Ray finger. In this scenario, the contribution of this article is twofold. At one end, we provide a general discrete Cosserat approach for the modeling of closed-chain soft robots which shares the geometrical structure of the rigid robotics counterpart. On the other end, the approach is employed to explore the family of Fin-Ray effect fingers. Finally, an improved design, which is able to conform to contacting surfaces, while maintaining stiffness out of its grasping plane, is fabricated and its performances are compared to those of a previously proposed prototype.
Cable-driven parallel robots (CDPRs) have attracted much attention due to their advantages, such as large workspace and excellent load capacity. However, their adaptability to different tasks has ...been limited because of fixed configurations. To improve this, a novel 3-DOF point-mass reconfigurable CDPR (RCDPR) has been designed, and its configuration can be changed by adjusting the positions of multiple cable anchors. Since wrench feasible workspace (WFW) is an essential criterion that describes the configuration characteristics, an optimal reconfiguration planning method is proposed to schedule the sequence and number of all movable cable anchors for adjusting the WFW range. Based on a two-level optimization process, the method can realize static reconfiguration (SR) or dynamic reconfiguration (DR) of the RCDPR. If SR cannot provide the required WFW by finding a static optimal configuration, the WFW range will be dynamically adjusted by DR. Besides, the number of movable cable anchors is minimized in DR by applying L 1 -norm optimization to the anchor velocity sequences. Simulations and experiments are implemented, and the results show that the proposed method can automatically determine when, which, and how the cable anchors move under physical constraints, and reducing the number of movable cable anchors can indeed save actuator energy effectively.
•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.
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.
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