Trajectory planning of free-floating space robot using Particle Swarm Optimization (PSO)

doi:10.1016/j.actaastro.2015.03.008

Acta Astronautica

Volume 112, July–August 2015, Pages 77-88

https://doi.org/10.1016/j.actaastro.2015.03.008 Get rights and content

Highlights

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Non-holonomic property of free-floating space robot is considered during its trajectory planning.
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Joint trajectories are parameterized by the Bézier curves for its simplicity and normalization.
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Constrained Particle Swarm Optimization algorithm with adaptive inertia weight is adopted to search for optimal solutions to construct the Bézier curves.
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The execution time of the joint motion is determined with respect to the joint velocity and acceleration boundaries.
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Multiple objectives optimization can be incorporated into the proposed trajectory planning method.

Abstract

This paper investigates the application of Particle Swarm Optimization (PSO) strategy to trajectory planning of the kinematically redundant space robot in free-floating mode. Due to the path dependent dynamic singularities, the volume of available workspace of the space robot is limited and enormous joint velocities are required when such singularities are met. In order to overcome this effect, the direct kinematics equations in conjunction with PSO are employed for trajectory planning of free-floating space robot. The joint trajectories are parametrized with the Bézier curve to simplify the calculation. Constrained PSO scheme with adaptive inertia weight is implemented to find the optimal solution of joint trajectories while specific objectives and imposed constraints are satisfied. The proposed method is not sensitive to the singularity issue due to the application of forward kinematic equations. Simulation results are presented for trajectory planning of 7 degree-of-freedom (DOF) redundant manipulator mounted on a free-floating spacecraft and demonstrate the effectiveness of the proposed method.

Introduction

The increasing demands of satellite maintenance, on-orbit assembly and space debris removal, etc. call for application of space robot to perform tasks in the particular harsh space environment. Examples include “Robot Technology Experiment (ROTEX)” [1], “Engineering Test Satellite VII (ETS-VII)” [2] and “Orbital Express (OE)” [3]. In light of the space robots currently planned by world wild space agencies, an increase in the number and the capacity of robot applied in space missions will be a foregone conclusion in the coming future [4]. In these space robotic programs, space missions executed under free-floating mode are of great interests to the researchers. However, space robot exhibits some special characteristics due to the dynamic coupling between the space manipulators and the spacecraft (base). Accordingly, particular trajectory planning techniques have to be developed to cope with the dynamic coupling issue of free-floating space robot.

In order to address the continuous path tracking issue of the end-effector, the concept of Generalized Jacobian Matrix (GJM) [5], Path Independent Workspace (PIW) [6], bidirectional path planning method [7] and Enhanced Disturbance Map (EDM) [8] was introduced for free-floating space robot. It is shown that the system states depend not only on the joint variables but also on the history of their trajectories. This introduces the so-called non-holonomic redundancy to the space robot. Another widely investigated method was Reaction Null-Space (RNS) as proposed in [9], [10], [11]. But the volume of RNS is limited especially for 6 DOF manipulators. Besides, trajectory planning of free-floating space robot can also be treated as an optimization issue. Various searching methods like variational approach [12], Genetic Algorithm (GA) [13], Particle Swarm Optimization (PSO) [14], [15], [16] and Sequential Quadratic Programming (SQP) [17] were employed to search the optimal solution to steer the end-effector of a free-floating space robot to a target pose.

This paper introduces a new method for trajectory planning issue of kinematically redundant manipulator while cope with joint range, velocity, acceleration limits with different objectives. The reason for choosing kinematically redundant manipulator is the existence of infinite solutions which can be employed for additional objectives, such as minimize base disturbance, avoid collision, or maximize the manipulability. In order to perform optimization, the joint trajectory is generally parametrized by polynomial functions [14], [15] or B-Spline [13], [17], however, it is not easy for above curves to deal with the imposed constraints. In this paper, the Bézier curve for its simplicity and normalization is used to represent the shape of joint trajectories and limit the values of joint range, rate, acceleration. PSO with adaptive inertia weight and various fitness functions and constraints is implemented to find the optimal solution for trajectory planning of free-floating space robot.

The rest of this paper is organized as follows: Section 2 introduces the kinematics and dynamics of free-floating space robotic system. Section 3 discusses the path planning issue and how to delineate this issue as an optimization problem. Section 4 depicts the concepts of PSO, fitness selection and constraints handling. Section 5 shows the simulation results of trajectory planning using PSO applied to a 7 DOF space robot. The conclusive remarks are listed in Section 6.

Section snippets

Kinematics and dynamics of space robot

Before discussion space robot in detail, some symbols and variables used in the following sections are listed in Table 1. A space robotic system is composed of a spacecraft and an n DOF manipulator, in total n+1 bodies as shown in Fig. 1. Many investigations have been conducted in the field of space robot dynamics. Refer to [9], [11], the dynamics equations of space robot using Lagrangian mechanism can be expressed as follows: $[\begin{matrix} H_{b} & H_{bm} \\ H_{bm}^{T} & H_{m} \end{matrix}] [\begin{matrix} {\ddot{x}}_{b} \\ \ddot{θ} \end{matrix}] + [\begin{matrix} c_{b} \\ c_{m} \end{matrix}] = [\begin{matrix} f_{b} \\ τ \end{matrix}] + [\begin{matrix} J_{b}^{T} \\ J_{e}^{T} \end{matrix}] f_{e}$

When no external force

Trajectory planning of space robot

The objective of trajectory planning is to generate applicable joint motion laws without violating the imposed constraints to complete the desired manipulators tasks [19]. Generally, a trajectory planning algorithm should have the following features:

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The specified objectives should be optimized under feasible regions.
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The continuity of the joint position, velocity should be guaranteed.
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Undesirable effects during motion should be minimized.

Particle Swarm Optimization

PSO is a stochastic search method yet with simpler philosophy. It was inspired by the coordinated motion of swarmed animals like flying birds and swimming fishes [22]. The states adjust of each particle in swarm takes into account the effect of stochastic, cognitive and social influence. A schematic diagram of the PSO with 4 particles is shown in Fig. 2. The PSO algorithm first initializes a population of particles with random initial values within the feasible searching space. The dimension of

Simulation results

The space robotic system used in this section is composed of a 6 DOF spacecraft and a 7 DOF kinematically redundant manipulator as shown in Fig. 1. The mass and inertia properties of the space robot are listed in Table 2, where $a_{i}$ , $b_{i}$ , and $I_{i}$ are expressed in its own body frame. The flow chart of the proposed algorithm is shown in Fig. 3. During the processing, the PSO algorithm first finds the optimal solution to construct the Bézier curve, after that, the execution time T is determined

Conclusions

Due to the dynamics coupling effect between the spacecraft and the manipulator, the determination of the end-effector pose relies not only on the current joint position, but also on the history motion of each joint. Therefore, the given end-effector pose cannot be handled only by inverse kinematics algorithm as fixed base manipulator. In this paper, a new trajectory planning method for free-floating space robot is proposed. Its main differences are as follows: (i) the non-holonomic property of

Acknowledgments

The authors gratefully acknowledge the support of the TUM Graduate School׳s Thematic Graduate/Faculty Graduate Center Mechanical Engineering at the Technische Universität Muenchen. The first author gratefully acknowledges the financial support of Chinese Scholarship Council (CSC No. 2010629015).

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Trajectory planning of free-floating space robot using Particle Swarm Optimization (PSO)

Highlights

Abstract

Introduction

Section snippets

Kinematics and dynamics of space robot

Trajectory planning of space robot

Particle Swarm Optimization

Simulation results

Conclusions

Acknowledgments

Autonomous capture of a tumbling satellite

J. Field Robot.

Resolved motion rate control of space manipulators with generalized Jacobian matrix

IEEE Trans. Robot. Autom.

Dynamic singularities in the control of free-floating space manipulators

ASME J. Dyn. Syst. Meas. Control

Nonholonomic path planning of space robot via a bidirectional approach

IEEE Trans. Robot. Autom.

On the global optimum path planning for redundant space manipulators

IEEE Trans. Syst. Man Cybern.