An adaptive discretized RNN algorithm for posture collaboration motion control of constrained dual-arm robots

Abstract

Although there are many studies on repetitive motion control of robots, few schemes and algorithms involve posture collaboration motion control of constrained dual-arm robots in three-dimensional scenes, which can meet more complex work requirements. Therefore, this study establishes the minimum displacement repetitive motion control scheme for the left and right robotic arms separately. On the basis of this, the design mentality of the proposed dual-arm posture collaboration motion control (DAPCMC) scheme, which is combined with a new joint-limit conversion strategy, is described, and the scheme is transformed into a time-variant equation system (TVES) problem form subsequently. To address the TVES problem, a novel adaptive Taylor-type discretized recurrent neural network (ATT-DRNN) algorithm is devised, which fundamentally solves the problem of calculation accuracy which cannot be balanced well with the fast convergence speed. Then, stringent theoretical analysis confirms the dependability of the ATT-DRNN algorithm in terms of calculation precision and convergence rate. Finally, the effectiveness of the DAPCMC scheme and the excellent convergence competence of the ATT-DRNN algorithm is verified by a numerical simulation analysis and two control cases of dual-arm robots.

Keywords: adaptive Taylor-type discretized recurrent neural network (ATT-DRNN); dual-arm posture collaboration motion control (DAPCMC); dual-arm robot; joint-limit conversion strategy; time-variant equation system (TVES).

Figure 1

The relationship between the ith joint angle ${\dot{\mathcal{z}}}_i(t)$ and the ith joint velocity ${\dot{\mathcal{z}}}_i(t)$ in the proposed JLCS (7)–(8), with i = 1, 2, ..., n.

Figure 2

Numerical simulation results of the ATT-DRNN (43), CTT-DRNN (36), and CET-DRNN in Wu and Zhang (2023) algorithms for addressing the TVQP problem (53), separately. (A) Status vector ℧(t) under inequality constraint generated by the ATT-DRNN algorithm (43) with a = −0.3 and δ = 2. (B) A(t)℧(t) under equality constraint c(t) obtained by the ATT-DRNN algorithm (43) with a = −0.3 and δ = 2. (C) RE ||e(t)||₂ generated by the ATT-DRNN algorithm (43) with a = −0.3 and different δ. (D) RE ||e(t)||₂ by three algorithms with different a and δ = 2. (E) Adaptive sampling period σ(t) with different δ. (F) Adaptive convergence factor ζ(t) with different δ.

Figure 3

The ATT-DRNN algorithm (43) controls the posture collaboration motion of the UR5 dual-arm robot with two arms placed on the contralateral side for the dual heart-shaped trajectory tracking. (A) Starting and terminal statuses of the dual-arm robot and the end-executor real and ideal trajectories in 3D space. (B) Outlines of real trajectory and ideal path in a 3D space. (C) Variations of the LA joint angles ${\mathcal{z}}_{\mathcal{L}}(t)$. (D) Variations of the RA joint angles ${\mathcal{z}}_{\mathcal{R}}(t)$. (E) Variations of the LA joint velocities ${\dot{\mho }}_{\mathcal{L}}(t)$. (F) Variations of the RA joint velocities ${\dot{\mho }}_{\mathcal{R}}(t)$. (G) Variations of the LA end-executor orientation $o_{\mathrm{\text{R}}\mathcal{L}}(t)$. (H) Variations of the RA end-executor orientation $o_{\mathrm{\text{R}}\mathcal{R}}(t)$. (I) The RE ||e(t)||₂ generated by three different algorithms.

Figure 4

Variations of the end-executor position error when the UR5 dual-arm robot with two arms placed on the contralateral side to achieve the posture collaboration motion for the dual heart-shaped trajectory tracking. (A) Generated by the ATT-DRNN algorithm (43). (B) Generated by the CTT-DRNN algorithm (36). (C) Generated by the CET-DRNN algorithm in Wu and Zhang (2023).

Figure 5

Snapshots of the UR5 dual-arm robot with two arms placed on the contralateral side during the trajectory tracking task of the dual heart-shaped path via the ATT-DRNN algorithm (43) solving the DAPCMC scheme (27)–(29). (A) Capturing at the starting moment. (B) Capturing at the intermediate moment. (C) Capturing at the terminal moment.

Figure 6

The ATT-DRNN algorithm (43) controls the posture collaboration motion of the UR5 dual-arm robot with two arms placed on the identical side for the heart-shaped and auspicious cloud trajectory tracking. (A) Starting and terminal statuses of the dual-arm robot and the end-executor real and ideal trajectories in a 3D space. (B) Outlines of real trajectory and ideal path in a 3D space. (C) Variations of the LA joint angles ${\mathcal{z}}_{\mathcal{L}}(t)$. (D) Variations of the RA joint angles ${\mathcal{z}}_{\mathcal{R}}(t)$. (E) Variations of the LA joint velocities ${\dot{\mho }}_{\mathcal{L}}(t)$. (F) Variations of the RA joint velocities ${\dot{\mho }}_{\mathcal{R}}(t)$. (G) Variations of the LA end-executor orientation $o_{\mathrm{\text{R}}\mathcal{L}}(t)$. (H) Variations of the RA end-executor orientation $o_{\mathrm{\text{R}}\mathcal{R}}(t)$. (I) The RE ||e(t)||₂ generated by three different algorithms.

Figure 7

Variations of the end-executor position error when the UR5 dual-arm robot with two arms placed on the identical side to achieve the posture collaboration motion for the heart-shaped and auspicious cloud trajectory tracking. (A) Generated by the ATT-DRNN algorithm (43). (B) Generated by the CTT-DRNN algorithm (36). (C) Generated by the CET-DRNN algorithm (Wu and Zhang, 2023).

Figure 8

Snapshots of the UR5 dual-arm robot with two arms placed on the identical side during the trajectory tracking task of the heart-shaped and auspicious cloud path via the ATT-DRNN algorithm (43) solving the DAPCMC scheme (27)-(29). (A) Capturing at the starting moment. (B) Capturing at the intermediate moment. (C) Capturing at the terminal moment.