Patrick Grosch

Motion planning for a novel reconfigurable parallel manipulator with lockable revolute joints

This paper introduces a class of reconfigurable parallel robots consisting of a fixed base and a moving platform connected by serial chains having RRP̲S (Revolute-Revolute-Prismatic-Spherical) topology. Only the prismatic joint is actuated and the first revolute joint in the chain can be locked or released online. The introduction of these lockable joints allow the prismatic actuators to maneuver to approximate 6-DoF motions for the moving platform. An algorithm for generating these maneuvers is first described. Then, a motion planner, based on the generation of a Probabilistic RoadMap (PRM) whose nodes are connected using the described maneuvers, is presented. The generated trajectories avoid singularities and possible collisions between legs. (See accompanying video)

Generation of Under-Actuated Manipulators With Nonholonomic Joints From Ordinary Manipulators

This paper shows how to generate under-actuated manipulators by substituting nonholonomic spherical pairs (nS pairs) for (holonomic) spherical pairs (S pairs) in ordinary (i.e. not under-actuated) manipulators. As a case study, an under-actuated manipulator, previously proposed by one of the authors, is demonstrated to be generated, through this pair substitution, from an inversion of the 6-3 fully-parallel manipulator (FPM). Moreover, the kinetostatic analysis of this under-actuated manipulator is reconsidered, and a simple and compact formulation is obtained. The results of this kinetostatic analysis can be used both in the design of the under-actuated manipulator, and in its control. Keywords: kinetostatics, non-holonomic constraint, ordinary manipulator, underactuated manipulator, parallel manipulator.

Uncalibrated Visual Servo for Unmanned Aerial Manipulation

This paper addresses the problem of autonomous servoing an unmanned redundant aerial manipulator using computer vision. The overactuation of the system is exploited by means of a hierarchical control law, which allows to prioritize several tasks during flight. We propose a safety-related primary task to avoid possible collisions. As a secondary task, we present an uncalibrated image-based visual servo strategy to drive the arm end-effector to a desired position and orientation by using a camera attached to it. In contrast to the previous visual servo approaches, a known value of camera focal length is not strictly required. To further improve flight behavior, we hierarchically add one task to reduce dynamic effects by vertically aligning the arm center of gravity to the multirotor gravitational vector, and another one that keeps the arm close to a desired configuration of high manipulability and avoiding arm joint limits. The performance of the hierarchical control law, with and without activation of each of the tasks, is shown in simulations and in real experiments confirming the viability of such prioritized control scheme for aerial manipulation.

A bilinear formulation for the motion planning of non-holonomic parallel orienting platforms

This paper deals with the motion planning problem for parallel orienting platforms with one non-holonomic joint and two prismatic actuators which can maneuver to reach any three-degree-of-freedom pose of the moving platform. Since any system with two inputs and up to four generalized coordinates can always be transformed into chained form, this path planning problem can be solved using well-established procedures. Nevertheless, the use of these procedures requires a good understanding of Lie algebraic methods whose technicalities have proven a challenge to many practitioners who are not familiar with them. As an alternative, we show how by (a) properly locating the actuators, and (b) representing the platform orientation using Euler parameters, the studied path planning problem admits a closed-form solution whose derivation requires no other tools than ordinary linear algebra.

A one-motor full-mobility 6-PUS manipulator

This paper presents the feasibility study of an under-actuated parallel manipulator with 6-PUS topology, destined to handle work-tables in CNC machine tools. The proposed device exploits the fact that, in such an application, the path between the initial and final poses of the mobile platform is not assigned to reduce the number of actuators to only one.

Geometric Path Planning Without Maneuvers for Nonholonomic Parallel Orienting Robots

Current geometric path planners for nonholonomic parallel orienting robots generate maneuvers consisting of a sequence of moves connected by zero-velocity points. The need for these maneuvers restrains the use of this kind of parallel robots to few applications. Based on a rather old result on linear time-varying systems, this letter shows that there are infinitely differentiable paths connecting two arbitrary points in SO(3) such that the instantaneous axis of rotation along the path rest on a fixed plane. This theoretical result leads to a practical path planner for nonholonomic parallel orienting robots that generates single-move maneuvers. To present this result, we start with a path planner based on three-move maneuvers, and then we proceed by progressively reducing the number of moves to one, thus providing a unified treatment with respect to previous geometric path planners.

Motion Planning for Parallel Robots with Non-holonomic Joints

Designing a robot manipulator with fewer actuators than the dimension of its configuration space – to reduce bulk, weight and cost – becomes feasible by introducing mechanical elements that lead to non-holonomic constraints. Unfortunately, the mechanical advantages of these non-holonomic designs are usually darkened by the complexity of their control. This paper deals with motion planning for parallel robots with non-holonomic joints shedding new light on their control strategies. As a case study, the motion planning problem is solved for a 3-ŬPU parallel robot, where Ŭ stands for a non-holonomic joint whose instantaneous kinematics are equivalent to that of a universal joint. It is thus shown how the three prismatic actuators can maneuver to reach any six-degree-of-freedom pose of the moving platform. The motion planning has been addressed as a control problem in the control system representation of the robot’s kinematics and a motion planning algorithm has been devised based on a Jacobian inversion of the end-point map of the representation. Performance of the algorithm is illustrated with numeric computations.

Generation of under-actuated parallel robots with non-holonomic joints and kinetostatic analysis of a case-study

It will be shown how to generate under-actuated manipulators by substituting non-holonomic spherical pairs (nS pairs) for (holonomic) spherical pairs (S pairs) in fully-parallel manipulators (FPMs). Through this pair substitution, an under-actuated manipulator, previously proposed by one of the authors, will be demonstrated to be generated from an inversion of the 6-3 FPM. Moreover, the kinetostatic analysis of this manipulator will be reconsidered to obtain a simple and compact formulation. This reformulated analysis can be used both in the design of the underactuated manipulator, and in its control.

Planning Setpoints for Contact Force Transitions in Regrasp Tasks of 3D Objects

This paper presents a simple and fast solution to the problem of finding the time variation of n contact forces that keep an object under equilibrium while one of the n contact forces is removed/added from/to the grasp. The object is under a constant perturbation force, like for instance its own weight. It is assumed no acceleration of the object during the regrasp operation, as well as the knowledge of the starting and ending grasp configurations. The procedure returns the set points of the n contact forces for a feed-forward control system of a manipulator device in a regrasping action. The procedure was implemented and an illustrative numerical example is included in the paper.

The HumanoidLab

Trabajo presentado a la 6th International Conference on Compute Supported Education, celebrada en Barcelona del 1 al 3 de abril de 2014.