Collision-free Motion Planning Of Redundant Manipulators Based On Dynamic Environmental Information

The application of redundant manipulators in unstructured working environments has attracted the attention of researchers for decades in the field of multi-robot collaboration,human-robot integration,on-orbit robotic systems,etc.Multi-manipulator collaborative assembly systems and human-robot collaboration systems can significantly improve the production efficiency,product quality,and flexibility of industrial production lines.Furthermore,in real applications,the redundant manipulators can avoid the interference caused by complex and dangerous workspaces,and then complete the tasks which are difficult for humans.The unpredictability and stochasticity of the complex working environments would cause a collision of the manipulator with its environment,which can lead to the sudden change in joint velocity and irreversible damage to hardware.Moreover,the motion performance,the safe workspace area,and the operability of manipulators will be significantly reduced during the interaction between manipulators and obstacles if the working environment is not properly modeled.In addition,the computation time of the inverse kinematics algorithm and the end effector motion planning algorithm need to satisfy the complex temporal requirements in a real-time control system.Therefore,safe and efficient motion planning in unstructured working environments needs to solve the problems,such as obstacle modeling,obstacle avoidance inverse kinematics solution,and feasible task-constrained motion planning of the end effector.In addition,these problems are very closely related due to the influence of the geometric configuration of manipulators and obstacles,the kinematic model and the function of motion control,etc.Therefore,to address these shortcomings,this paper studies the inverse kinematics algorithm of the redundant manipulators and the motion planning method of the end effector based on the dynamic information of the working environments.First,we provide the obstacle avoidance inverse kinematics algorithms of the 7 degrees of freedom(DOF)redundant and hyper-redundant manipulators.Second,we present an obstacle avoidance motion planning algorithm of the end effectors.Then the simulation and physical platforms for different application scenarios are established.Finally,the proposed inverse kinematics algorithms and motion planning algorithm are verified on the physical Baxter robot and the Harbin Institute of Technology hyper-redundant robot.Based on the task space constraints,the joint limits constraints,and the collision-free constraints,this paper presents an obstacle avoidance inverse kinematics algorithm of the7-DOF redundant manipulators based on the Newton-Raphson iteration method and firstorder optimization method.In addition,to prevent the redundant manipulator from getting close to Jacobian singularities,we can find a better initial joint configuration through random joint values over a standard uniform distribution number on the joint limits.To avoid collision of the manipulators during operation,the proposed algorithm can compute the obstacle avoidance inverse kinematics solution based on the given task of the end effector and the geometry and motion information feedback of the obstacles.Moreover,a detailed proof of the convergence of the collision constraint factor of this algorithm is given according to the Lipschitz continuity condition and ?-smooth condition,and a rigorous stability analysis is also performed on the algorithm based on the Lyapunov equation.Finally,a simulation system of the 7-DOF manipulators is established based on the robot operating system and the Gazebo robot simulator,then the feasibility and effectiveness of the algorithm are verified through the simulations and performance analysis.To simplify the calculation process of inverse kinematics solution and improve the computational efficiency,this paper presents a collision-free inverse kinematics algorithm of the hyper-redundant manipulators based on the heuristic method.The proposed algorithm uses the forward and reverse iterative search of the joint position variation of the hyper-redundant manipulator to solve the task constraints.Then,we introduce an obstacle avoidance adjustment strategy of the velocity of the links based on the closed Minkowski sum and velocity conversion between joints and links of the manipulator.This algorithm can avoid complex matrix calculations and reduce the computation time effectively.In addition,the solution process is based on the joint position vector,which can avoid the singular problem of the Jacobian matrix.Moreover,we will show that our approach is applicable to solve the collision-free inverse kinematics problem of soft robots.We highlight the performance of the proposed algorithm in simulated environments that contain a hyper-redundant manipulator and many moving or static obstacles.The simulation results demonstrate the effectiveness and versatility of this approach.Furthermore,we also present a detailed comparative analysis of our algorithm and other existing inverse kinematics algorithms.To achieve application requirements,such as obstacle avoidance motion planning and fine operation ability of the end effector,this paper introduces more complex superquadric objects to extend the closed Minkowski sum between spheres and ellipsoids.A generalized obstacle avoidance motion planning method of the end effector based on a linear motion equation is proposed.In addition,the collision detection method between ellipsoids and superquadrics surface is given.Moreover,based on the Monte Carlo method,an algorithm for solving the outer tangent of a complex curved surface is designed.The proposed motion planning algorithm is extended based on the typical working environments,which including an environment with multiple static obstacles and an environment with one dynamic obstacle.These extensions show that our algorithm can be applied to real-time obstacle avoidance motion planning of the end effector and can deal with the uncertainty of geometric and motion information of the working environments.Furthermore,we also consider the impact of translation and rotation velocity of the end effector and obstacles on the safe operation workspace.We present the results of various simulation experiments in the two-dimensional and three-dimensional workspaces to highlight the performance of our algorithm.To further highlight the performance and efficiency of the algorithm,comparisons with some existing obstacle avoidance motion planning approaches are provided.To validate the effectiveness of the inverse kinematics algorithms of the 7-DOF redundant and hyper-redundant manipulators and the motion planning algorithm of the end effector,based on the Baxter robot and the Harbin Institute of Technology hyperredundant robot system,we designed three experiments,including obstacle avoidance inverse kinematics of the 7-DOF redundant manipulator;collision-free inverse kinematics of the hyper-redundant manipulator;obstacle avoidance motion planning of the end effector.These experiments are implemented in various physical experiments to verify the effectiveness and practicability of the algorithms which have been presented in this paper.