An $L_{0}$-Norm-Based Sparse Projection Neural Network for Cooperative Motion of Dual-Arm Robots Under Physical Constraints

Abstract

Sparsification techniques aim to reduce data density by extracting essential features from high-dimensional data, thereby lowering computational and storage demands while enhancing model efficiency and generalization. In the collaborative control of dual-arm robots, promoting sparsity in joint-angle velocities helps minimize the number of active joints, thereby reducing energy consumption and the risk of collisions. Although the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{0}$</tex-math></inline-formula>-norm provides an exact measure of sparsity by counting nonzero elements, its minimization is an NP-hard problem. Therefore, recent studies have employed alternative norms (e.g., the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{1}$</tex-math></inline-formula>-norm) to promote sparsity in joint-angle velocities. However, these alternatives often struggle to achieve consistently high levels of sparsity. To overcome this limitation, a novel <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{0}$</tex-math></inline-formula>-norm-based sparse projection neural network (LS-PNN) is proposed for dual-arm robotic cooperation under physical constraints. Unlike existing approaches, the LS-PNN preserves the sparsity representation accuracy of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{0}$</tex-math></inline-formula>-norm while avoiding its inherent NP-hard problem. The stability of the LS-PNN is theoretically verified. Simulation and physical robot experiments demonstrate that our proposed LS-PNN significantly outperforms other state-of-the-art schemes when dealing with the sparsity of joint-angle velocities under handling constraints.