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

Path Coordination Planning and Control in Robotic Material Handling and Processing

This chapter presents a unified approach to coordination planning and control for robotic position and orientation trajectories in Cartesian space and its applications in robotic material handling and processing. The unified treatment of the end-effector positions and orientations is based on the robot pose ruled surface concept and used in trajectory interpolations. The focus of this chapter is on the determination and control of the instantaneous change laws of position and orientation, i.e., the generation and control of trajectories with good kinematics and dynamics performances along such trajectories. The coordination planning and control is implemented through controlling the motion laws of two end points of the orientation vector and calculating the coordinates of instantaneous corresponding points. The simulation and experiment in robotic surface profiling/finishing processes are presented to verify the feasibility of the proposed approach and demonstrate the capabilities of planning and control models. Keywords: Robot pose ruled surface, Unified approach, Trajectory planning and control, Off-line programming, Robotics polishin

Minimum-time path planning for robot manipulators using path parameter optimization with external force and frictions

This paper presents a new minimum-time trajectory planning method which consists of a desired path in the Cartesian space to a manipulator under external forces subject to the input voltage of the actuators. Firstly, the path is parametrized with an unknown parameter called a path parameter. This parameter is considered a function of time and an unknown parameter vector for optimization. Secondly, the optimization problem is converted into a regular parameter optimization problem, subject to the equations of motion and limitations in angular velocity, angular acceleration, angular jerk, input torques of actuators’, input voltage and final time, respectively. In the presented algorithm, the final time of the task is divided into known partitions, and the final time is an additional unknown variable in the optimization problem. The algorithm attempts to minimize the final time by optimizing the path parameter, thus it is parametrized as a polynomial of time with some unknown parameters. The algorithm can have a smooth input voltage in an allowable range; then all motion parameters and the jerk will remain smooth. Finally, the simulation study shows that the presented approach is efficient in the trajectory planning for a manipulator that wants to follow a Cartesian path. In simulations, the constraints are respected, and all motion variables and path parameters remain smooth

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