Numerical approach of collision avoidance and optimal control on robotic manipulators

Collision-free optimal motion and trajectory planning for robotic manipulators are solved by a method of sequential gradient restoration algorithm. Numerical examples of a two degree-of-freedom (DOF) robotic manipulator are demonstrated to show the excellence of the optimization technique and obstacle avoidance scheme. The obstacle is put on the midway, or even further inward on purpose, of the previous no-obstacle optimal trajectory. For the minimum-time purpose, the trajectory grazes by the obstacle and the minimum-time motion successfully avoids the obstacle. The minimum-time is longer for the obstacle avoidance cases than the one without obstacle. The obstacle avoidance scheme can deal with multiple obstacles in any ellipsoid forms by using artificial potential fields as penalty functions via distance functions. The method is promising in solving collision-free optimal control problems for robotics and can be applied to any DOF robotic manipulators with any performance indices and mobile robots as well. Since this method generates optimum solution based on Pontryagin Extremum Principle, rather than based on assumptions, the results provide a benchmark against which any optimization techniques can be measured

A randomized kinodynamic planner for closed-chain robotic systems

Kinodynamic RRT planners are effective tools for finding feasible trajectories in many classes of robotic systems. However, they are hard to apply to systems with closed-kinematic chains, like parallel robots, cooperating arms manipulating an object, or legged robots keeping their feet in contact with the environ- ment. The state space of such systems is an implicitly-defined manifold, which complicates the design of the sampling and steering procedures, and leads to trajectories that drift away from the manifold when standard integration methods are used. To address these issues, this report presents a kinodynamic RRT planner that constructs an atlas of the state space incrementally, and uses this atlas to both generate ran- dom states, and to dynamically steer the system towards such states. The steering method is based on computing linear quadratic regulators from the atlas charts, which greatly increases the planner efficiency in comparison to the standard method that simulates random actions. The atlas also allows the integration of the equations of motion as a differential equation on the state space manifold, which eliminates any drift from such manifold and thus results in accurate trajectories. To the best of our knowledge, this is the first kinodynamic planner that explicitly takes closed kinematic chains into account. We illustrate the performance of the approach in significantly complex tasks, including planar and spatial robots that have to lift or throw a load at a given velocity using torque-limited actuators.Peer ReviewedPreprin

Autonomous space processor for orbital debris

The development of an Autonomous Space Processor for Orbital Debris (ASPOD) was the goal. The nature of this craft, which will process, in situ, orbital debris using resources available in low Earth orbit (LEO) is explained. The serious problem of orbital debris is briefly described and the nature of the large debris population is outlined. The focus was on the development of a versatile robotic manipulator to augment an existing robotic arm, the incorporation of remote operation of the robotic arms, and the formulation of optimal (time and energy) trajectory planning algorithms for coordinated robotic arms. The mechanical design of the new arm is described in detail. The work envelope is explained showing the flexibility of the new design. Several telemetry communication systems are described which will enable the remote operation of the robotic arms. The trajectory planning algorithms are fully developed for both the time optimal and energy optimal problems. The time optimal problem is solved using phase plane techniques while the energy optimal problem is solved using dynamic programming

A New Approach to Time-Optimal Path Parameterization based on Reachability Analysis

Time-Optimal Path Parameterization (TOPP) is a well-studied problem in robotics and has a wide range of applications. There are two main families of methods to address TOPP: Numerical Integration (NI) and Convex Optimization (CO). NI-based methods are fast but difficult to implement and suffer from robustness issues, while CO-based approaches are more robust but at the same time significantly slower. Here we propose a new approach to TOPP based on Reachability Analysis (RA). The key insight is to recursively compute reachable and controllable sets at discretized positions on the path by solving small Linear Programs (LPs). The resulting algorithm is faster than NI-based methods and as robust as CO-based ones (100% success rate), as confirmed by extensive numerical evaluations. Moreover, the proposed approach offers unique additional benefits: Admissible Velocity Propagation and robustness to parametric uncertainty can be derived from it in a simple and natural way.Comment: 15 pages, 9 figure

Critically fast pick-and-place with suction cups

Fast robotics pick-and-place with suction cups is a crucial component in the current development of automation in logistics (factory lines, e-commerce, etc.). By "critically fast" we mean the fastest possible movement for transporting an object such that it does not slip or fall from the suction cup. The main difficulties are: (i) handling the contact between the suction cup and the object, which fundamentally involves kinodynamic constraints; and (ii) doing so at a low computational cost, typically a few hundreds of milliseconds. To address these difficulties, we propose (a) a model for suction cup contacts, (b) a procedure to identify the contact stability constraint based on that model, and (c) a pipeline to parameterize, in a time-optimal manner, arbitrary geometric paths under the identified contact stability constraint. We experimentally validate the proposed pipeline on a physical robot system: the cycle time for a typical pick-and-place task was less than 5 seconds, planning and execution times included. The full pipeline is released as open-source for the robotics community.Comment: 7 pages, 5 figure

Time-Optimal Trajectory Planning with Interaction with the Environment

Optimal motion planning along prescribed paths can be solved with several techniques, but most of them do not take into account the wrenches exerted by the end-effector when in contact with the environment. When a dynamic model of the environment is not available, no consolidated methodology exists to consider the effect of the interaction. Regardless of the specific performance index to optimize, this article proposes a strategy to include external wrenches in the optimal planning algorithm, considering the task specifications. This procedure is instantiated for minimum-time trajectories and validated on a real robot performing an interaction task under admittance control. The results prove that the inclusion of end-effector wrenches affect the planned trajectory, in fact modifying the manipulator's dynamic capability.Comment: \copyright 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other work

Optimal time trajectories for industrial robots with torque, power, jerk and energy consumed constraints

This article is (c) Emerald Group Publishing and permission has been granted for this version to appear here https://riunet.upv.es/. Emerald does not grant permission for this article to be further copied/distributed or hosted elsewhere without the express permission from Emerald Group Publishing Limited.[EN] Purpose - The purpose of this paper is to analyze the impact of the torque, power, jerk and energy consumed constraints on the generation of minimum time collision-free trajectories for industrial robots in a complex environment. Design/methodology/approach - An algorithm is presented in which the trajectory is generated under real working constraints (specifically torque, power, jerk and energy consumed). It also takes into account the presence of obstacles (to avoid collisions) and the dynamics of the robotic system. The method solves an optimization problem to find the minimum time trajectory to perform the tasks the robot should do. Findings - Important conclusions have been reached when solving the trajectory planning problem related to the value of the torque, power, jerk and energy consumed and the relationship between them, therefore enabling the user to choose the most efficient way of working depending on which parameter he is most interested in optimizing. From the examples solved the authors have found the relationship between the maximum and minimum values of the parameters studied. Research limitations/implications - This new approach tries to model the real behaviour of the actuators in order to be able to upgrade the trajectory quality, so a lot of work has to be done in this field. Practical implications - The algorithm solves the trajectory planning problem for any industrial robot and the real characteristics of the actuators are taken into account, which is essential to improve the performance of it. Originality/value - This new tool enables the performance of the robot to be improved by combining adequately the values of the mentioned parameters (torque, power, jerk and consumed energy).This paper has been made possible thanks to support from the Spanish Ministry of Science and Innovation, through the Project for Research and Technological Development, ref. DPI2010-20 814-C02-01.Rubio Montoya, FJ.; Valero Chuliá, FJ.; Suñer Martinez, JL.; Cuadrado Iglesias, JI. (2012). Optimal time trajectories for industrial robots with torque, power, jerk and energy consumed constraints. Industrial Robot: An International Journal. 39(1):92-100. doi:10.1108/01439911211192538]S9210039