The time-optimal trajectory planning problem involves minimizing the time required to follow a path defined in space, subject to kinematic and dynamic constraints. Here, we introduce a novel technique, called the bisection algorithm (BA), which is fully implemented in C++ and extends dynamic programming approaches to the problem. These approaches, which rely on dividing the global problem into a series of simpler subproblems, become increasingly advantageous compared to direct transcription methods as the number of problem constraints increases. In contrast to nearly all other dynamic programming approaches, BA does not rely on finding a maximum-velocity curve or explicitly finding acceleration switching points during the trajectory planning process. Additionally, only one forward and one backward integration are used, during which all constraints are imposed. This approach is made feasible through careful control of the numerical integration process and the use of a bisection algorithm to resolve constraint violations during integration. BA is shown to be significantly simpler, faster, and more robust than recently proposed algorithms: a direct comparison is made for a series of paths to be followed by a serial manipulator, subject to kinematic constraints. The wide applicability of BA is then established by solving the time-optimal problem for a parallel manipulator following a complex path, subject to both kinematic and dynamic constraints.

This paper proposes a point-to-point dynamic trajectory planning technique for reaching a series of poses with a six-degree-of-freedom (six-DOF) cable-suspended parallel robot. Each trajectory segment is designed to have zero translational and rotational velocity at its endpoints; transitions between segments have translational and rotational acceleration continuity. This formulation facilitates the synthesis of trajectories that extend beyond the static workspace of the robot. A basis motion is introduced, which is a mathematical function that can be adapted for each coordinate direction along each trajectory segment. Kinematic constraints are satisfied through the selection of the coefficients for this function. Dynamic constraints are imposed by defining feasible regions within the workspace for each segment endpoint, based on the previous endpoint. Spherical linear interpolation (SLERP) is used to produce singularity-free, optimally interpolated rotational trajectory segments. An experimental implementation is presented using a six-DOF prototype and a supplementary video file is included to demonstrate the results.

This paper proposes a dynamic trajectory planning technique for six-degree-of-freedom (6-DOF) cable-suspended parallel robots (CSPRs). First, a passive mechanical system that is equivalent to the CSPR is introduced to provide insight and facilitate the design of trajectories that can extend beyond the robot's static workspace. The tilt-and-torsion angle convention is used to develop the mathematical model and impose restrictions for the rotational component of the trajectories. The dynamic differential equations that govern the translational component of the trajectories are shown to become linear under some conditions. Natural frequencies of an equivalent passive linear system of constant-stiffness springs are, thus, obtained and the set of linear differential equations associated with this system is integrated to produce a general solution for natural, periodic trajectories. This approach is used to produce pure translation trajectories and more complex motion that includes changes in position and orientation. An experimental implementation is also presented using a 6-DOF prototype and a supplementary video file is included to demonstrate the results.

A fundamental problem with many solid freeform fabrication systems is the production of large dimensional errors, due to the freeform construction process. The subject of this paper is surface mapping feedback (SMF), a closed-loop technique for minimizing the dimensional errors produced by rapid prototyping systems. The main steps of the technique are presented, namely part measurement, control implementation, and deposition adjustment. A test platform, the Cobra 600 rapid freeze prototyping system, is used to validate SMF. A helical gear part is constructed first with open-loop control and then with SMF control; system performance and part quality are compared for the two cases.

Ice has long been used by humankind for utilitarian purposes, and more recently for artistic and entertainment purposes. Nowadays, the field of ice construction is becoming more commercially relevant, with increased interest in ice modeling at the small scale, and in ice tourism, specifically ice hotels at the large scale. As a result, there is a market for automating ice construction, and building detailed structures that would otherwise require a significant amount of manual work. To address this demand, the authors are currently developing experimental robotic systems for building ice structures: the Fab@home, for building small-scale structures, and the Adept Cobra 600 robot, for building medium-scale structures. Further software and hardware development is needed for the Cobra, since it was not designed for rapid prototyping, and certainly not for rapid prototyping using ice as the working material. The authors have designed and built fluid delivery systems for each machine to permit the use of water as the building material. A signal-processing subsystem permits control of the water-delivery flow rate and synchronization with the robot motion. Additionally, we have developed a slicing algorithm to generate toolpaths for the Cobra using stereolithography (STL) files as the input. We also intend to develop a larger robotic system for producing ice sculptures and buildings at the architectural scale.