Motion paths of cable-driven hexapods must carefully be planned to ensure that the lengths and tensions of all cables remain within acceptable limits, for a given wrench applied to the platform. The cables cannot go slack-to keep the control of the robot-nor excessively tight-to prevent cable breakage-even in the presence of bounded perturbations of the wrench. This paper proposes a path-planning method that accommodates such constraints simultaneously. Given two configurations of the robot, the method attempts to connect them through a path that, at any point, allows the cables to counteract any wrench lying in a predefined uncertainty region. The configuration space, or C-space for short, is placed in correspondence with a smooth manifold, which facilitates the definition of a continuation strategy to search this space systematically from one configuration, until the second configuration is found, or path nonexistence is proved by exhaustion of the search. The force Jacobian is full rank everywhere on the C-space, which implies that the computed paths will naturally avoid crossing the forward singularity locus of the robot. The adjustment of tension limits, moreover, allows to maintain a meaningful clearance relative to such locus. The approach is applicable to compute paths subject to geometric constraints on the platform pose or to synthesize free-flying motions in the full 6-D C-space. Experiments illustrate the performance of the method in a real prototype.

The analysis of singularities is central to the development and control of a manipulator. However, existing methods for singularity set computation still concentrate on specific classes of manipulators. The absence of general methods able to perform such computation on a large class of manipulators is problematic because it hinders the analysis of unconventional manipulators and the development of new robot topologies. The purpose of this paper is to provide such a method for nonredundant mechanisms with algebraic lower pairs and designated input and output speeds. We formulate systems of equations that describe the whole singularity set and each one of the singularity types independently, and show how to compute the configurations in each type using a numerical technique based on linear relaxations. The method can be used to analyze manipulators with arbitrary geometry, and it isolates the singularities with the desired accuracy. We illustrate the formulation of the conditions and their numerical solution with examples, and use 3-D projections to visualize the complex partitions of the configuration space induced by the singularities.

This paper provides an algorithm for computing singularity-free paths on closed-chain manipulators. Given two nonsingular configurations of the manipulator, the method attempts to connect them through a path that maintains a minimum clearance with respect to the singularity locus at all points, which guarantees the controllability of the manipulator everywhere along the path. The method can be applied to nonredundant manipulators of general architecture, and it is resolution complete. It always returns a path whenever one exists at a given resolution or determines path nonexistence otherwise. The strategy relies on defining a smooth manifold that maintains a one-to-one correspondence with the singularity-free C-space of the manipulator, and on using a higher dimensional continuation technique to explore this manifold systematically from one configuration, until the second configuration is found. If desired, the method can also be used to compute an exhaustive atlas of the whole singularity-free component reachable from a given configuration, which is useful to rapidly resolve subsequent planning queries within such component, or to visualize the singularity-free workspace of any of the manipulator coordinates. Examples are included that demonstrate the performance of the method on illustrative situations.

This paper provides an algorithm for computing singularity-free paths on non-redundant closed-chain manipulators. Given two non-singular configurations of the manipulator, the method attempts to connect them through a configuration space path that maintains a minimum clearance with respect to the singularity locus at all points. The method is resolution-complete, in the sense that it always returns a path if one exists at a given resolution, or returns “failure” otherwise. The path is computed by defining a new manifold that maintains a one-to-one correspondence with the singularity-free configuration space of the manipulator, and then using a higher-dimensional continuation technique to explore this manifold systematically from one configuration, until the second configuration is found. Examples are included that demonstrate the performance of the method on illustrative situations.

This paper provides a method to compute all types of singularities of non-redundant manipulators with non-helical lower pairs and designated instantaneous input and output speeds. A system of equations describing each singularity type is given. Using a numerical method based on linear relaxations, the configurations in each type are computed independently. The method is general and complete: it can be applied to manipulators with arbitrary geometry; and will isolate singularities with the desired accuracy. As an example, the entire singularity set and its complete classification are computed for a two-degree-of-freedom mechanism. The complex partition of the configuration space by various singularities is illustrated by three-dimensional projections.

This paper introduces a new method for workspace boundary determination on general structure manipulators. The method uses a branch-and-prune technique to isolate a set of output singularities and then classifies the points on such a set according to whether they correspond to motion impediments in the workspace. A detailed map of the workspace is obtained as a result, where all interior and exterior regions, together with the singularity and barrier sets that separate them, get clearly identified. The method can deal with open- or closed-chain manipulators, whether planar or spatial, and is able to take joint limits into account. Advantages over previous general methods based on continuation include the ability to converge to all boundary points, even in higher dimensional cases, and the fact that manual guidance with a priori knowledge of the workspace is not required. Examples are included that show the performance of the method on benchmark problems documented in the literature, as well as on new ones unsolved so far.