Nonholonomic Mobile Platform Research Articles

Time-optimal trajectory planning for a rigid formation of nonholonomic mobile platforms

AbstractThis paper presents a method for planning time-optimal trajectories for a formation of multiple nonholonomic (heavy duty) platforms (HDPs) to cooperatively transport an object to a specified pose. The first part addresses the mobile platforms themselves while the second part provides a trajectory planning approach derived from the well-known virtual leader approach. In order to ensure proper transport of the shared payload, the vehicles are modeled individually, resulting in a formation control problem. The goal of the optimization process is to minimize a cost function that balances time optimality, smooth control signals, and formation rigidity. The optimal control problem (OCP) takes into account the kinematics of the vehicles as well as their physical limitations. It is solved by using a multiple shooting method, which yields the desired trajectories for all vehicles while ensuring smooth control signals. The paper includes optimization results for several scenarios involving two and three HDPs together with various target poses, demonstrating the effectiveness of the proposed method.

Torque control of a wheeled humanoid robot with dual redundant arms

Most of conventional controllers are prone to consume more computational time for controlling a wheeled humanoid robot. A nonlinear trajectory control of a wheeled humanoid robot using a model-based controller with less computational load and energy consumption is presented in this article. The upper body of the humanoid robot consists of two 6 degrees of freedom redundant arms, a three degrees of freedom torso and a two degrees of freedom neck. The nonholonomic mobile platform consists of two actuated wheels and two caster wheels. Nonlinearity of the robot dynamic model and coupling between various branches of the upper body are taken into account. The dynamic model derived using Newton–Euler approach along with decoupled Natural Orthogonal Complement matrix approach is used to derive dynamic equations of the upper body and the wheeled platform. Zero moment point based stability approach is used for verifying stable motion of the wheeled humanoid robot with minimum energy and time consumption to complete a task. The proposed computed torque controller is compared with other similar controllers developed for the same robot model to prove advantages of the proposed torque controller. Simulation results are experimentally validated with the real robot.

Hierarchical finite-time cooperative control for teleoperation of networked disturbed mobile manipulators

This paper investigates the teleoperation problem of networked disturbed mobile manipulators (NDMMs), in which the human operator remotely controls multiple slave mobile manipulators through a master manipulator. Each individual of the slave ones consisted of a nonholonomic mobile platform and a holonomic constrained manipulator that is mounted on the nonholonomic mobile platform. The cooperative control objective of the considered teleoperation problem includes: (1) synchronizing the states of the slave manipulators to the human-controlled master one; (2) forcing the mobile platforms of the slave ones to form a user-defined formation; (3) controlling the geometric center of all the platforms to track a reference trajectory. We present a hierarchical finite-time cooperative control (HFTCC) framework to achieve the cooperative control goal in a finite time. The presented framework includes the distributed estimator, the weight regulator and the adaptive local controller, where the estimator generates the estimated states of the desired formation and trajectory, the regulator selects the slave robot that the master one needs to track, as well as the presented adaptive local controller guarantees the finite-time convergence of the controlled states with model uncertainties and disturbances. Additionally, for improving the telepresence, a novel super twisting observer is presented to reconstruct the interaction force between the salve mobile manipulators and the remote operating environment on the master (i.e., the human) side. Finally, the effectiveness of the proposed control framework is demonstrated by several simulation results.

Potential Field Control of a Redundant Nonholonomic Mobile Manipulator with Corridor-Constrained Base Motion

This work proposes a solution for redundant nonholonomic mobile manipulator control with corridor constraints on base motion. The proposed control strategy applies an artificial potential field for base navigation to achieve joint control with desired trajectory tracking of the end effector. The overall kinematic model is created by describing the nonholonomic mobile platform and the kinematics of the manipulator. The objective function used consists of a primary control task that optimizes the joint variables to achieve the desired pose or trajectory of the end effector and a secondary control task that optimizes the joint variables for the base to support the arm and stay within the corridor. As a last priority, an additional optimization is introduced to optimize the maneuverability index. The proposed baseline navigation has global convergence without local minima and is computationally efficient. This is achieved by an optimal grid-based search on a coarse discrete grid and a bilinear interpolation to obtain a continuous potential function and its gradient. The performance of the proposed control algorithm is illustrated by several simulations of a mobile manipulator model derived for a Pal Tiago mobile base and an Emiko Franka Panda robotic manipulator.

Design Hybrid Iterative Learning Controller for Directly Driving the Wheels of Mobile Platform against Uncertain Parameters and Initial Errors

In this paper, we develop a hybrid iterative learning controller (HILC) for a non-holonomic wheeled mobile platform to achieve trajectory tracking with actual complex constraints, such as physical constraints, uncertain parameters, and initial errors. Unlike the traditional iterative learning controller (ILC), the control variable selects the rotation speed of two driving wheels instead of the forward speed and the rotation speed. The hybrid controller considers the physical constraints of the robot’s motors and can effectively handle the uncertain parameters and initial errors of the system. Without the initial errors, the hybrid controller can improve the convergence speed for trajectory tracking by adding other types of error signals; otherwise, the hybrid controller achieves trajectory tracking by designing a signal compensation for the initial errors. Then, the effectiveness of the proposed hybrid controller is proven by the relationship between the input, output, and status signals. Finally, the simulations demonstrate that the proposed hybrid iterative learning controller effectively tracked various trajectories by directly controlling the two driving wheels under various constraints. Furthermore, the results show that the controller did not significantly depend on the system’s structural parameters.

Fixed Time Synchronization Control for Bilateral Teleoperation Mobile Manipulator With Nonholonomic Constraint and Time Delay

In this brief, the fixed time synchronization control is investigated for nonholonomic mobile manipulator teleoperation system. The mobile manipulator is divided into two subsystems for analysis, which are nonholonomic mobile platform and holonomic constrained manipulator. Coupling terms between two subsystems are considered as disturbances. A fixed time synchronization controller is proposed to deal with the parameter uncertainties and unknown bounded disturbances. Lyapunov stability theory guarantees the stability of the closed-loop teleoperation system. Numerical simulations verify the effectiveness of the proposed results.

Robust Adaptive Sliding Mode Controller for a Nonholonomic Mobile Platform

In this paper, a robust adaptive sliding mode controller is designed for a mobile platform trajectory tracking. The mobile platform is an example of a nonholonomic mechanical system. The presence of holonomic constraints reduces the number of degree of freedom that represents the system model, while the nonholonomic constraints reduce the differentiable degree of freedom. The mathematical model was derived here for the mobile platform, considering the existence of one holonomic and two nonholonomic constraints imposed on system dynamics. The partial feedback linearization method was used to get the input-output relation, where the output is the error functions between the position of a certain point on the platform and the desired path. The dynamic error model was considered uncertain and subjected to friction torques on the wheels. The adaptive sliding mode control was utilized to design a robust controller, that will force the platform to follow the desired trajectory. The simulation of the proposed controller was done via MATLAB to reveal the ability of the robust adaptive sliding mode controller applied as a trajectory tracker for various path shapes.

Dynamic modeling of flexible cooperative mobile manipulator with revolute-prismatic joints for the purpose of moving common object with closed kinematic chain using the recursive Gibbs–Appell formulation

In this paper, the dynamic equations of flexible cooperative manipulators that are kinematically and dynamically constrained to an object and are placed on a non-holonomic mobile platform are explored. The main objective is to develop the dynamics of closed kinematic cooperative manipulators by defining constraints in mobile form while considering the geometric dimensions of the common object instead of assuming a concentrated mass in the gripper as well as the application of manipulator with flexible links and revolute-prismatic joints in the constrained cooperative mobile form. Unlike robots with independent manipulators, the dynamic constraint relates the dynamic equations of object and arms, initiating the motion and introducing interaction forces from the object to arms. In addition, the kinematic constraint keeps the distance between the two arms constant by constraining the relative motion velocity of the arms’ gripper. The dynamic equations of manipulators are derived using the recursive Gibbs–Appell formulation while the object equations are obtained using the Newton-Euler approach. Finally, the motion equations for a cooperative mobile robot with two 2-flexible-link arms are simulated. The results are evaluated at two stages by incorporating dynamic constraints as well as concurrent consideration of kinematic and dynamic constraints. Also, each manipulator's dynamic model weighted by using the experimental test setup with single link and revolute-prismatic joint.

LOW COST COLLISION AVOIDANCE SYSTEM ON HOLONOMIC AND NON- HOLONOMIC MOBILE ROBOTS

Technological advancement in industries necessitates development in autonomous mobile robots with obstacle avoidance for applications in industries, hospitals and educational environment. Holonomic motion allows the mobile robots to move instantaneously in any direction with no constraints while non-holonomic motion restricts the motion in limited directions. This study presents the comparison of obstacle avoidance performance using low cost sensors on holonomic and non-holonomic mobile robots. The robot prototypes are developed and implemented with stable control system for better mobility. Experimental results show that the omnidirectional mobile robots avoid collisions with limited space and less time while non-holonomic mobile platforms exhibits reduced computational complexity and efficient implementation. The developed mobile robots can be used for diverse task specification applications. Article DOI: https://dx.doi.org/10.20319/mijst.2019.51.1222 This work is licensed under the Creative Commons Attribution-Non-commercial 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/4.0/ or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.

Trajectory Tracking and Stability Analysis for Mobile Manipulators Based on Decentralized Control

SummaryTrajectory tracking of a mobile manipulator in the Cartesian space based on decentralized control is considered in this paper. The dynamic model is first rearranged to take the form of two interconnected subsystems with constraint flow, namely, a nonholonomic mobile platform subsystem and a holonomic manipulator subsystem. Secondly, using the inverse kinematics, the workspace desired trajectory of the mobile manipulator is transformed to the manipulator joint space as well as the platform desired trajectory. The kinematic control is developed from the desired trajectory of the platform. Then, the desired velocity is derived using the kinematic controller of the mobile platform, after which the velocity is used to obtain the control law of the mobile platform subsystem. Thirdly, the control law of the manipulator subsystem is developed based on the desired and real values of the manipulator, as well as the desired velocity. According to the Lyapunov stability theory, the proposed decentralized control strategy guarantees the global stability of the closed-loop system, and the tracking errors are bounded. Experimental results obtained on a 3-DOF manipulator mounted on a mobile platform are given to demonstrate the feasibility and effectiveness of the proposed approach. This is confirmed by a comparison with the computed torque approach.

Rapid Navigation Function Control for Two-Wheeled Mobile Robots

This paper presents a kinematic controller for a differentially driven mobile robot. The controller is based on the navigation function (NF) concept that guarantees goal achievement from almost all initial states. Slow convergence in some cases is a significant disadvantage of this approach, especially when narrow passages exist in the environment and/or specific values of design parameters are set. The main reason of this phenomenon is that the velocity control strongly depends on the slope of the NF. The algorithm proposed in this paper is based on a method introduced in Urakubo (Nonlin. Dyn. 81(3): 1475–1487 2015), that extends NF to nonholonomic mobile platforms and allows stabilizing not only the position of robots but also their orientation. This algorithm is used as a reference in experimental performance comparison. In the new algorithm, the gradient of the NF is used to generate motion direction but the velocity is computed as a function of position and orientation errors. This approach results in much better state converge. Analysis of the convergence shows how the location of the eigenvalues of linearized system affects time of goal achievement. The paper describes saddle point detection and avoidance methodology and presents their experimental verification. It also shows what happens in practice if initial position is located exactly in the saddle point and its detection/avoidance procedures are turned off.

Tracking control for non-holonomic mobile manipulator using decentralised control strategy

This paper presents a tracking control strategy for a non-holonomic mobile manipulator using a decentralised control strategy. The mobile manipulator is viewed as an interconnection of two subsystems - a non-holonomic mobile platform subsystem and a holonomic manipulator subsystem. First, a kinematic controller of the two-wheel driven mobile platform is developed to obtain a desired velocity. Second, a distributed control strategy is developed in order to track a desired trajectory in the joint space. This desired trajectory is obtained from the workspace trajectory using the inverse kinematics. The distributed control strategy consists of controlling the manipulator, starting from the last joint and going backwards until the first joint. Each joint is controlled while assuming that the remaining joints and the platform are stable and follow their desired trajectories. The stability of the system is proved using Lyapunov theory. These controllers are tested on a three degrees-of-freedom mobile manipulator and compared with the computed torque approach. The experimental and simulation results present a good tracking which shows the effectiveness of this control strategy.

Tracking control for non-holonomic mobile manipulator using decentralised control strategy

This paper presents a tracking control strategy for a non-holonomic mobile manipulator using a decentralised control strategy. The mobile manipulator is viewed as an interconnection of two subsystems - a non-holonomic mobile platform subsystem and a holonomic manipulator subsystem. First, a kinematic controller of the two-wheel driven mobile platform is developed to obtain a desired velocity. Second, a distributed control strategy is developed in order to track a desired trajectory in the joint space. This desired trajectory is obtained from the workspace trajectory using the inverse kinematics. The distributed control strategy consists of controlling the manipulator, starting from the last joint and going backwards until the first joint. Each joint is controlled while assuming that the remaining joints and the platform are stable and follow their desired trajectories. The stability of the system is proved using Lyapunov theory. These controllers are tested on a three degrees-of-freedom mobile manipulator and compared with the computed torque approach. The experimental and simulation results present a good tracking which shows the effectiveness of this control strategy.

Dynamically consistent Jacobian inverse for mobile manipulators

ABSTRACTBy analogy to the definition of the dynamically consistent Jacobian inverse for robotic manipulators, we have designed a dynamically consistent Jacobian inverse for mobile manipulators built of a non-holonomic mobile platform and a holonomic on-board manipulator. The endogenous configuration space approach has been exploited as a source of conceptual guidelines. The new inverse guarantees a decoupling of the motion in the operational space from the forces exerted in the endogenous configuration space and annihilated by the dual Jacobian inverse. A performance study of the new Jacobian inverse as a tool for motion planning is presented.

Robust adaptive tracking control for nonholonomic mobile manipulator with uncertainties

In this paper, mobile manipulator is divided into two subsystems, that is, nonholonomic mobile platform subsystem and holonomic manipulator subsystem. First, the kinematic controller of the mobile platform is derived to obtain a desired velocity. Second, regarding the coupling between the two subsystems as disturbances, Lyapunov functions of the two subsystems are designed respectively. Third, a robust adaptive tracking controller is proposed to deal with the unknown upper bounds of parameter uncertainties and disturbances. According to the Lyapunov stability theory, the derived robust adaptive controller guarantees global stability of the closed-loop system, and the tracking errors and adaptive coefficient errors are all bounded. Finally, simulation results show that the proposed robust adaptive tracking controller for nonholonomic mobile manipulator is effective and has good tracking capacity.

Force-guidance of a compliant omnidirectional non-holonomic platform

Physical guidance is a natural interaction capability that would be beneficial for mobile robots. However, placing force sensors at specific locations on the robot limits where physical interaction can occur. This paper presents an approach that uses torque data from four compliant steerable wheels of an omnidirectional non-holonomic mobile platform, to respond to physical commands given by a human. The use of backdrivable and torque-controlled elastic actuators for active steering of this platform intrinsically provides the capability of perceiving applied forces directly from its locomotion mechanism. In this paper, we integrate this capability into a control architecture that allows users to force-guide the platform with shared-control ability, i.e., having the platform being guided by the user while avoiding obstacles and collisions. Results using a real platform demonstrate that user’s intent can be estimated from the compliant steerable wheels, and used to guide the platform while taking nearby obstacles into consideration.

Lyapunov-based nonlinear controllers for obstacle avoidance with a planar [formula omitted]-link doubly nonholonomic manipulator

A mobile manipulator is a robotic system made up of two components; a mobile platform and a manipulator mounted on the platform equipped with non-deformable wheels. Such a combined system requires complex design and control. This paper considers the autonomous navigation problem of a nonholonomic mobile platform and an n-link nonholonomic manipulator fixed to the platform. For this planar n-link doubly nonholonomic manipulator, we present the first ever set of nonlinear continuous controllers for obstacle avoidance. The controllers provide a collision-free trajectory within a constrained workspace cluttered with fixed obstacles of different shapes and sizes whilst satisfying the nonholonomic and kinodynamic constraints associated with the robotic system. An advantage of the proposed method is the ease at which the acceleration-based control laws can be derived from the Lyapunov function. The effectiveness of the nonholonomic planner is demonstrated via computer simulations.

Cooperative Object Path Following Control by means of Mobile Manipulators: a Switched Systems Approach

This paper proposes a switched control algorithm for distributed cooperative manipulation of rigid bodies in a planar setting. More specifically, we consider the problem of making a grasped object follow a desired position and orientation path. The system contains N robots, possibly of heterogeneous designs, each of which consists of a manipulator arm and a nonholonomic mobile platform. Control is based on local information, is carried out on a kinematic level and partly utilizes inverse kinematics. We use Lyapunov-like arguments to prove that the algorithm is almost globally stable and also show that its parameters can be chosen so that any input saturation level is met. The time between certain switches is proved to be bounded below, and the system is shown to be free of any Zeno behavior.

Autonomous Control of a Mobile Manipulator

This paper considers the design of a motion planner that will simultaneously accomplish control and motion planning of a n-link nonholonomic mobile manipulator, wherein, a n-link holonomic manipulator is coupled with a nonholonomic mobile platform, within an obstacle-ridden environment. This planner, derived from the Lyapunov-based control scheme, generates collision-free trajectories from an initial configuration to a final configuration in a constrained environment cluttered with stationary solid objects of different shapes and sizes. We demonstrate the efficiency of the control scheme and the resulting acceleration controllers of the mobile manipulator with results through computer simulations of an interesting scenario.

Efficiency of Double Nonholonomic Mobile Manipulators

Abstract This paper deals with the problem of defining performance measures of doubly nonholonomic mobile manipulators composed of a nonholonomic mobile platform and a nonholonomic manipulator mounted on the platform. We introduce the kinematic theory of such mobile manipulators in frame of the endogenous configuration space approach, which assumes that: the kinematics of mobile manipulators is represented by a pair of driftless control systems driven by platform and manipulator controls, and sharing output function that describes position and orientation of the end-effector; the kinematic performance measures refer to the analytic Jacobian of the system; a locally controllable system yields nontrivial performance measures. Our results consist in a definition of the following local performance characteristics: the dexterity ellipsoid, the local dexterity, the energy efficiency and the motion efficiency. The usefulness of new local measures is demonstrated on the example of determining efficient configurations of a 3 d.o.f. planar nonholonomic manipulator fixed to a kinematic car type platform.