Safe Motion Planning for Imprecise Robotic Manipulators by Minimizing Probability of Collision

In recent years, a number of trajectory optimization algorithms have been proposed and established for motion planning of robot manipulators in complex, but static, predefined environments. To enable reactive motion planning under uncertain conditions caused, for example, by moving obstacles, this paper proposes a formulation of the trajectory optimization problem that is tailored for model predictive control. The proposed algorithmic solution leverages off-the-shelf computational tools for nonlinear model predictive control, optimization, and collision checking. In addition, a motion planning paradigm is introduced to allow for online collision-free motion when following a joystick command. The approach is validated in the context of an industrial pick-and-place application using MATLAB® and a Kinova® robot manipulator, both in simulation and with actual hardware.

PurposeThe purpose of this paper is to present a new nested rapidly‐exploring random tree (RRT) algorithm for fault tolerant motion planning of robotic manipulators.Design/methodology/approachAnother RRT algorithm is nested within the general RRT algorithm. This second nested level is used to check whether the new sampled node in the first nested level is fault tolerant. If a solution can be found in the second nested RRT, the reduced manipulator after failures at the new sampled node can still fulfill the remaining task and this new sampled node is added into the nodes of RRT in the first level. Thus, the nodes in the first level RRT algorithm are all fault tolerant postures. The final trajectory joined by these nodes is also obviously fault tolerant. Besides fault tolerance, this new nested RRT algorithm also can fulfill some secondary tasks such as improvement of dexterity and obstacle avoidance. Sufficient simulations and experiments of this new algorithm on fault tolerant motion planning of robotic manipulators are implemented.FindingsIt is found that the new nested RRT algorithm can fulfill fault tolerance and some other secondary tasks at the same time. Compared to other existing fault tolerant algorithms, this new algorithm is more efficient.Originality/valueThe paper presents a new nested RRT algorithm for fault tolerant motion planning.

This paper describes the use of the probabilistic motion planning technique SBL "single-query bidirectional probabilistic algorithm with lazy collision checking" or in motion planning for robot manipulators. We present a novel strategy to remedy the PRM "probabilistic roadmap" paths which are both excessively long and discontinuous in velocity and acceleration. The optimization of the path will be done first through coarse optimal lazy A* optimization and then through a fine cutting-triangles-edge one, the edges discontinuities are smoothed with cubic polynomials taking the robot's specific dynamic and cinematic constraints. The whole strategy is applied to the 6 axes robot Manipulator MOTOMAN SV3X.

Different from general linear inequality or equality, the problem of future different-level linear inequality and equality (FDLLIE) is investigated, which is much more interesting and challenging. In order to solve this difficult FDLLIE, continuous different-level linear inequality and equality (CDLLIE) is first considered. A zeroing equivalency theorem is proposed based on the zeroing neural network method, and then a continuous solution model is, thus, obtained for CDLLIE solving. Furthermore, a new discrete-solution (NDS) model is developed for FDLLIE solving by using a proposed new 7-instant Zhang et al. discretization (ZeaD) formula to discretize the continuous solution model. Meanwhile, theoretical analyses and results are presented to show the excellent properties of the NDS model. Numerical results illustrate the effectiveness and superiority of the NDS model for solving FDLLIE. Furthermore, application experiments for motion planning of robot manipulator are conducted to substantiate the efficacy of the NDS model for FDLLIE solving.

This paper presents a new inverse kinematics algorithm of 6-DOF robot manipulator via the analytic solution with Conformal Geometric Algebra (CGA). To simplify the calculation, angles of joints 1, 5 and 6 are obtained using the analytic method. On the other hand, the remaining joint angles θ 2 , θ 3 and θ 4 are figured out by CGA which describes the geometric relationship intuitively. The proposed method is verified and simulated in Matlab and Rviz, respectively. Experimental results show the high accuracy of proposed approach. Moreover, it can be easily integrated in the motion planning of robot manipulator.

The investigations repor ted at this sympos ium are in the process of publication elsewhere [1, 2]; since the la t te r papers are r a the r detailed, we will content ourselves here with a ra ther brief survey of the work, with only a few addit ional results. The t e rm (~ Monte Carlo ,) has come into use to designate numerical methods in which specifically stochastic elements are introduced, in contras t to the whole body of classical numerical techniques which consist of numerical evaluations of complete ly de te rminan t algebraic expressions. The par t icular Monte Carlo me thod used here was devised by METROPOHS et al. [3]; its essential fea ture is t ha t i t produces a Markov chain [4] in which the individual 5 Ia rkov s tates are points in the usual configuration space of s tat is t ical mechanics, for a sys tem of N molecules confined a t a t e m p e r a t u r e T in ~ volume Y. The t ransi t ion probabil i t ies character izing the Markov chain are de termined in such a way tha t the va lue of any funct ion of configuration state, averaged over all s tates developed in the Markov cha.in, approaches the pe t i t canonical ensemble average value of the same function. I t should be noticed t ha t the present me thod does no t consist in an evaluat ion of the configurational phase in tegral b y means of a random, selection of points in configuration space. A me thod of the l a t t e r sort, which m a y be compared with a sequence of independent throws of a die, is indeed

Real-time motion planning and control of multi-joint robot manipulators are studied using neural networks. The proposed neural network approach consists of two modules: one for real-time collision-free motion planning, the other for real-time fine control of the robot manipulators. The motion planning module is a biologically inspired, parallel connected, topologically organised neural network, where each neuron is characterised by a shunting equation, whose state space is the robot configuration joint space. This module is capable of planning a real-time optimal path for robot manipulators through the dynamic activity landscape of the neural network. The motion control module involves of a feedforward neural network together with a traditional PD feedback loop. It is capable of achieving real-time fine motion control of robot manipulators under significant uncertainties and without any prior knowledge of the robot dynamics. This module can quickly compensate sudden changes in the robot dynamics. The real-time fine control of robot manipulators is achieved through the online learning of the neural network. Both the motion planning and motion control modules are computationally efficient, and their global stabilities are proved using Lyapunov stability theory.

Objectives. The work analyzes features of one of the most promising approaches to solve the problems for motion planning of autonomous robotic manipulators of various types and purposes using the rapidly exploring random tree (RRT) method. The development of modern robotics is shown to be inextricably linked with the improvement of the designs of the created samples, for which the placement of a manipulator on platform becomes a typical layout option. Prospects for using the RRT method as a constructive basis for creating a universal motion planner are evaluated for mobile and robotic manipulators, including autonomous robotic systems with a manipulator on a moving platform.Methods. The object of the research is the RRT method and its well-known modifications RRT* and RRT-Connect. The effectiveness of applying such methods for solving problems associated with planning the motions of robotic manipulators of various types was evaluated using computer and natural simulation methods.Results. Based on a review of the literature and the results of the research, the wide possibilities of the RRT method can be used for solving motion planning problems not only for mobile and robotic manipulators, but also for robotic systems on whose transport platform an onboard manipulator has been installed (including those having a redundant or reconfigurable structure). The effectiveness of the applied application of the RRT method is confirmed by examples of modeling a mobile platform with an onboard manipulator and the results of full-scale experiments with a prototype of the ARAKS reconfigurable mechatronic-modular robotic manipulators (RTU MIREA, Russia). It can be experimentally demonstrated and theoretically substantiated that the final dimension of the exploring tree, and hence the time of its construction up to reaching a given target state, is largely determined by the value of the growth factor.Conclusions. The generalization of the results obtained opens up real prospects for using the RRT method as a constructive basis not only for creating universal means for motion planning mobile robotic systems with an onboard manipulator, but also for solving the problems of automating the docking of autonomous mobile platforms.

Presents an approach to sensor-based obstacle modeling in a configuration space for manipulator motion planning in unknown environments. In order to achieve this objective, an efficient algorithm is used to fast map obstacles based on defined fundamental obstacles in the workspace and their images in the configuration space. A robotic manipulator is assumed to be equipped with distance sensors to detect obstacles in the local region. By computation of the critical points of an obstacle based on information acquired by the distance sensors, an obstacle model in the configuration space is constructed. By using this sensor-based configuration space modeling, robot motion planning in unknown environments can be performed in realistic time frames.

The problem of the global Lagrangian description of a dynamical system which has a global Hamiltonian description is considered; the motion of a charged particle in the field of a static magnetic monopole is a prototype of such dynamical problems. The symplectic structure on the (cotangent bundle of the) manifold is associated with a closed but not necessarily exact two-form. In conventional language this means that the tensor field inverse to the symplectic metric is divergence free but not necessarily expressible globally as the curl of a vector field; and hence the usual passage to Hamilton's principle and the Lagrangian can be carried out in patches but not necessarily globally. Generalizing techniques developed elsewhere, we show that the fundamental expression for the action integral is like the surface integral of the closed but not necessarily exact antisymmetric tensor field (two-form) rather than like the line integral of a vector field (one-form). This naturally leads to the path-space formalism in which the action functional depends not only on a point in configuration space but also a path from a chosen fixed point terminating in the relevant point in configuration space. We then show how this is a universal unfolding and how the topological obstructions in the configuration-space description are circumvented in the path-space description. The path-space description contains redundancies and they can be reduced; locally the new manifold is obtained by associating an angle of rotation [a U(1) fiber] with each configuration-space point, but globally there would be a nontrivial fiber-bundle structure. These questions naturally carry over to the quantum theory of such systems and it is shown how quantization conditions arise. The structure of the quantum-theory formalism for such systems is analyzed. The considerations are applied to the monopole problem where the enlarged space in which the Lagrangian description is possible is explicitly identified as the manifold of the group SU(2).

Omni-directional Wheeled Mobile Robots (Omni-WMR) are holonomic system able to move sideways. They have locomotive advantage and are widely deployed in a larger range of application fields, especially in narrowly constrained service-styled manufacturing industries. To ensure smooth motion and full development of locomotive advantages, motion planning draws great attention. Thanks to the mechanism of powered caster wheel (PCW), the motion of Omni-WMR can be decoupled. The collective motion can be decomposed into dimensions of x, y and θ, then planned independently and superposed. In this way trajectory can be planned in the Cartesian space, and later on transformed to the joint space through inverse instantaneous kinematics model for actuation of the motor at each joint. Quintic-polynomial interpolation is used for the case of start to goal with only initial and final configurations known, and piecewise-cubic-spline interpolation is applied for the case of a sequence of intermediate way-points known in the configuration space as input. Here the geometric points for the robot to go through are assumed to be known as a priori without loss of generality. The approaches are implemented in python on ROS (Robot Operating System), and these modular ROS packages are tested on a physical Omni-WMR developed at our lab. Meanwhile, these ROS packages are also tested equivalently in a virtual simulation environment modelled using ROS stage simulator. The experimental results have proved that the motion planning algorithms are able to generate smooth velocity profile for the robot to achieve the goal, which have validated the effectiveness of these algorithms.

VLSI-efficient schemes for high-speed construction of tangent graph

Definitions Symmetry operations leave a set of objects in indistinguishable configurations which are said to be equivalent . A set of symmetry operators always contains at least one element, the identity operator E . When operating with E the final configuration is not only indistinguishable from the initial one, it is identical to it. A proper rotation , or simply rotation , is effected by the operator R ( φ n ), which means “carry out a rotation of configuration space with respect to fixed axes through an angle φ about an axis along some unit vector n .” The range of φ is − π φ ≤ π . Configuration space is the three-dimensional (3-D) space ℛ 3 of real vectors in which physical objects such as atoms, molecules, and crystals may be represented. Points in configuration space are described with respect to a system of three space-fixed right-handed orthonormal axes x , y , z , which are collinear with OX, OY, OZ (Figure 2.1(a)). (A right-handed system of axes means that a right-handed screw advancing from the origin along OX would rotate OY into OZ, or advancing along OY would rotate OZ into OX, or along OZ would rotate OX into OY.) The convention in which the axes x , y , z remain fixed, while the whole of configuration space is rotated with respect to fixed axes, is called the active representation .

Traditional motion planning can be computationally burdensome for practical robots, due to extensive collision checking and considerable iterative propagation of cost values. We present a novel neural network architecture which can directly generate the cost-to-go (c2g) function for a given configuration space and a goal configuration. The output of the network is a continuous function whose gradient in configuration space can be directly used to generate trajectories in motion planning without the need for protracted iterations or extensive collision checking. This higher order function (i.e. a function generating another function) representation lies at the core of our motion planning architecture, c2g-HOF, which can take a workspace as input, and generate the cost-to-go function over the configuration space map (C-map). Simulation results for 2D and 3D environments show that c2g-HOF can be orders of magnitude faster at execution time than methods which explore the configuration space during execution. We also present an implementation of c2g-HOF which generates trajectories for robot manipulators directly from an overhead image of the workspace.

Double manipulator path planning is the basis for overhead line live working robot to complete the task. The previous dual manipulator motion path planning method has some problems, such as low success rate, low convergence speed, unstable guidance, and easy to lead to path discontinuity in complex environment. Therefore, this paper proposes a decoupling motion planning method for two manipulators of live working robot based on hybrid RRT (Rapidly-Exploring Random Trees) algorithm. The hybrid RRT algorithm combines target offset RRT algorithm, bidirectional RRT algorithm and dynamic expansion RRT algorithm. MATLAB robot toolbox is used to simulate the motion path planning of 6-DOF double manipulator of overhead line live working robot. The results show that the method proposed in this paper can realize the loose coupling and efficient collision free motion planning of double manipulator of live working robot.