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Jerk Optimized Motion Planning of Redundant Space Robot Based on Grey-Wolf Optimization Approach

  • Research Article-Mechanical Engineering
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Abstract

In the joint space, calculating the jerk-optimized trajectory of a redundant space manipulator is a significant issue in motion planning. The third derivative of desired joint trajectory position, known as a jerk, influences the smooth and effective movement of the manipulator. Using the conventional approach for multi-parameters selection, it is challenging to get an optimal solution. This can be taken care of by using an advanced optimization technique, grey wolf optimization which provides such search capabilities having the potential to produce optimum results. Therefore, to implement jerk-optimized motion planning, this work presents an approach based on grey wolf optimization, constrained by the joint inter-knot parameters in the joint space. It is expected that the proposed approach will impart the lowest joint jerk in comparison with other existing approaches like the genetic algorithm and particle swarm optimization. Consequently, minimal deviation of the joint trajectory can be observed at each joint. For various time intervals, minimal jerk values of the mean, maximum, and minimum for all joint angles are experienced compared to the genetic algorithm approach. Hence, smooth joint trajectories are generated for each joint, enabling the end-effector to move the desired pose with minimal jerk enhancing the stability of the manipulator.

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Abbreviations

\(H_{b} ,H_{bm}\) :

Inertia matrix and coupling inertia matrix for robot base, respectively

\(\vec{\theta }_{1} ,\vec{\theta }_{2} , \ldots ,\vec{\theta }_{8}\) :

Joint angle vector of the manipulator

\(y_{eo}\), \(y_{ed}\), \(\theta^{e}\) :

Starting, desired pose, orientation of end-effector, respectively

\(r_{o} ,r_{e}\) :

Position vector of the centroid of robot base and end-effector, respectively

\(d_{c}\) :

Initial pose of manipulator base

\(\dot{\phi }\), \(\dot{\theta }\) :

Angular velocity of the base and effector, respectively

\(\dot{T}_{e}\), \(\dot{p}\) :

Translational and joint velocity of end effector, respectively

\(\psi\) :

Euler angles

\(\varsigma\), \(\tau^{ * }\) :

Normalized time, real time of jth trajectory segment

\(a_{i}\) :

Position vector from joint \(j_{i}\) to mass centre of link (\(c_{i}\))

\(b_{i}\) :

Position vector from mass centre of link (\(c_{i}\)) to joint \(j_{i + 1}\)

\(\alpha ,\beta ,\delta\) :

Different layers of grey wolves

\(\vec{A}_{p}\) :

Optimal position of grey wolves with optimized fitness value

\(t\) :

Total number of iterations

\(\vec{X}(t)\), \(\vec{X}(t + 1)\), \(\vec{X}_{w} (t)\) :

Position of first grey wolf, denotes position of next grey wolves after (t + 1) iterations, position of \(\alpha ,\beta ,\delta\) grey, wolves, respectively

\(\vec{N},\vec{P}\) :

Vectors for updated position of grey wolves

\(\vec{y}_{1} ,\vec{y}_{2}\) :

Random vectors in range of [0, 2]

\(\vec{n}\) :

Vectors in range of [0, 5]

\(\vec{X}_{\alpha } ,\vec{X}_{\beta } ,\vec{X}_{\delta }\) :

Updated position of \(\alpha ,\beta ,\delta\) grey wolves after hunting

\(A_{\alpha }\), \(A_{\beta }\), \(A_{\delta }\) :

Optimal position for \(\alpha ,\beta ,\delta\) grey wolves after hunting

\(\dot{u}_{c} ,\ddot{u}_{c}\) :

Velocity and acceleration of each joint, respectively

GWO:

Grey wolf optimization

GA:

Genetic algorithm

GJM:

Generalized Jacobian matrix

EDM:

Enhanced disturbance map

BPP:

Bidirectional path planning

PIW:

Path independent workspace

RNS:

Reaction null space

HDC:

Hybrid dynamic coupling

OTPJS:

Optimum trajectory planning in joint space

PDW:

Path dependent workspaces

DOF:

Degree of freedom

PSO:

Particle swarm optimization

OTG:

Optimal trajectory generation

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Authors and Affiliations

  1. National Institute of Technology Jamshedpur, Jamshedpur, 831014, India

    Abhishek Shrivastava & Vijay Kumar Dalla

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  1. Abhishek Shrivastava
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  2. Vijay Kumar Dalla
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Correspondence to Abhishek Shrivastava.

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Appendix

Appendix

See Tables 3, 4, 5 and 6.

Table 3 Jerk estimation for various time intervals using linear segment polynomial blend (joint jerk)
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Table 4 Jerk estimation for various time intervals using GA approach (joint jerk)
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Table 5 Jerk estimation for various time intervals using GWO approach (joint jerk)
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Table 6 The mean, maximum, and minimum jerk values for various time intervals
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Shrivastava, A., Dalla, V.K. Jerk Optimized Motion Planning of Redundant Space Robot Based on Grey-Wolf Optimization Approach. Arab J Sci Eng 48, 2687–2699 (2023). https://doi.org/10.1007/s13369-022-07002-1

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