A deformable, flexible sheet that is held by multiple robots can be used for manipulating and transporting an object. For such multi-robot collaborative transporting system, forward kinematics provide object's potential positions where it might remain stationary on the sheet. Some of these forward kinematics solutions are however demonstrated unstable under object's position or robot formation perturbations. This paper presents stability criteria of the kinematics solutions of the object on the deformable sheet held by multi-robot system. We capture the sheet deformation and object position using the virtual variable cable model. A constrained quadratic problem is formulated to obtain the forward kinematics solution for a given multi-robot configuration. Linear dependence of active constraints and stability multipliers are used to assess the stability of the kinematics solutions. Two stability criteria are proposed and analyzed under object position or robot formation perturbations. These criteria are related to the properties and conditions of the stability multipliers. We present an efficient computational algorithm to determine stable kinematics, which are a small fraction of feasible solutions. Experimental results and case studies are presented to validate and demonstrate the effectiveness and efficiency of the analyses and algorithms.

The parametric array loudspeaker produces highly directional sound via a nonlinear process in air, which also introduces inherent baseband distortions. However, conventional recursive modulators employed to compensate for nonlinearity demand substantially increased bandwidth and are not optimized for speech applications. In this paper, we propose a deep learning method tailored for speech, called DeepPreNet. It contains two parts: a pre-processing network (PreNet) and a forward inference model (ForwModel). The ForwModel is a pre-trained network using real recorded speeches to model the actual nonlinear process, enhancing its reliability for PreNet training. The PreNet is trained to generate pre-processed signals, which are subsequently fed into the ForwModel to recover the distortion-free speech. By leveraging the harmonic-rich feature of speech, the proposed method incorporates distortions to reconstruct clean speech, thereby alleviating the bandwidth constraints imposed by the transducer. Experiments in both near- and far-field conditions demonstrate that the proposed method achieves remarkable performance compared to refined baseline techniques with the real transducer response.

The parametric array loudspeaker inherently introduces baseband distortions in directional sound applications due to the nonlinear process in air. Recently, DNNs have been used to model this forward process and to generate preprocessed signals for distortion-free speech restoration. However, when trained on real-world audio, the preprocessing network can exploit weaknesses in the forward model, producing adversarial outputs. To address it, we propose a reorganization strategy for the two-stage framework, comprising a causal TF-GridNet for preprocessed signal generation and a modified time-frequency (T-F) domain differential Volterra Filter (DiffVF) as the forward model. The causal TF-GridNet estimates real and imaginary components using a T-F band-split mechanism. The modified forward model integrates the second-order difference and kernel convolution operations of the original time-domain version into the T-F domain, preserving interpretability while stabilizing training. A refined$N$th-order equalization, based on the T-F domain DiffVF model, is implemented as a competitive baseline. Simulated and real-world experiments demonstrate state-of-the-art reconstruction performance of the proposed method across various objective metrics.