NON-HOLONOMIC MOBILE MANIPULATOR KINEMATIC CONTROL using HYBRID SIMULATED ANNEALING Arjun Bhasin Mechanical Engineering IIT Kanpur, India Email: arjunbhasin.pec@gmail.com Rekha Raja Mechanical Engineering IIT Kanpur, India Email: rekhar@iitk.ac.in Ashish Dutta Mechanical Engineering IIT Kanpur, India Email: adutta@iitk.ac.in Abstract—This paper proposes a global optimization based kinematic control of a 6 DOF non-holonomic mobile manipulator having a 3 DOF PUMA like arm, by optimizing smoothness and the Velocity Transformation Ratio (VTR) over the entire trajectory to achieve a control which executes a given end-effector task. The proposed approach involves formulating the functionals of the chosen objectives over the path and optimizing the same using Hybrid Simulated Annealing (HSA) algorithm for faster convergence to global minimum. The method generates smooth trajectories for the mobile manipulator without violating the non- holonomic constraint of the robot, which are optimized globally. Simulations of test cases are provided to establish the efficacy of the method in generating globally optimized trajectories. I. I NTRODUCTION A mobile manipulator refers to a robotic platform with a mounted robotic arm, which combines the mobility of the former with the manipulation ability of the latter. Such a system has many applications in planetary surface exploration, military and industrial operations and household robotics. The system generally has more number of degrees of freedom than are required to execute the task. This allows for dexterity at the cost of control complexity. Over the past few decades, three important methods have been developed for redundancy resolution and motion plan- ning of mobile manipulators (1) Extended Jacobian [1] (2) Projected Gradient [2] and (3) Operational space extension [3]. These methods also allow for optimization of a secondary objective along with the primary task of following a given trajectory. Several secondary objectives like manipulability, singularity avoidance [4], joint angle limits [5] [6], etc. have been used. The main drawback of these methods is that they optimize the secondary objective locally and do not ensure global optimality over the entire trajectory. This paper addresses the redundancy resolution and global objective optimization of a 6 DOF redundant non-holonomic mobile manipulator with a 3 DOF PUMA like robotic-arm, over the entire desired trajectory using HSA [7] to execute a given end-effector task. Functionals capturing smoothness and VTR are developed and optimized over the entire trajectory. The HSA method ensures faster global convergence and proper search space exploration. Results showing the efficacy of the method are given. The software was developed using open- source C++ libraries like Eigen [8] and Visualization Tool Kit [9]. II. SYSTEM MODELLING AND ANALYSIS A. Kinematic Modelling Let R be the ground frame of reference. We consider a mobile manipulator with a differential drive (unicycle) platform having a 3 DOF PUMA like robotic arm. Let the configuration variable of the mobile manipulator be given as q ∈ℜ 6 , with q =[q p ,q a ] T , where q p =[x, y, φ] T is the platform configuration and q a =[q a1 ,q a2 ,q a3 ] T is the arm configuration. Let ξ be the operational space parameter. We ignore rotations and only consider the position of the end- effector, hence ξ =[x, y, z] T ∈ℜ 3 . The forward kinemat- ics maps the configuration space to the operational space ξ = f (q)= f (x, y, φ, q a1 ,q a2 ,q a3 ) where f is a non-linear function. Fig.1 shows the frame assignment on the mobile manipulator and the forward kinematics is formulated using the D-H Parameters [10]. Fig. 1: Frame Assignment To derive the instantaneous kinematic model, we need to consider the non-holonomic constraint (rolling without slip- ping). The non-holonomic constraint reduces the dimensional- ity of the velocity space while not reducing the dimensionality of the configuration space. Let the control input to the mobile manipulator be given as u =[u p ,u a ] T =[v, ω, ˙ q a1 , ˙ q a2 , ˙ q a3 ] T , where v and ω are the platform velocity (along the sagittal 2015 IEEE International WIE Conference on Electrical and Computer Engineering (WIECON-ECE) 19-20 December 2015, BUET, Dhaka, Bangladesh 978-1-4673-8786-6/15/$31.00 ©2015 IEEE 435