Heavy quadrupedal drives have great potential for overcoming obstacles, showing great possibilities for transportation industries in complex environments. Ground reaction force (GRF) is a crucial state variable for quadrupedal control. Most GRF observations are implemented in lightweight quadrupeds, with little consideration of the loading being static or slippery on the body. However, the load information is vital to the heavy-duty quadruped applied in transportation tasks. In this paper, we disassembled the whole-body dynamics into the body dynamics combined with the individual floating single-leg dynamics and completed observing the virtual coupling effects between the body and legs. Based on the observed coupling force and centroidal dynamics (CD), the GRF of a stance leg is obtained without the awareness of body weight, movement, and load information. Furthermore, we utilized the body dynamics and the observed virtual force to obtain the body's unknown payload. By reconstructing the moment balance equation, we obtained the payload's position concerning the body coordinate. Compared to conventional quadrupedal GRF observation methods, this framework achieves higher observation accuracy in heavy quadrupeds without load and body information. Additionally, it enables real-time calculation of load magnitude and position.

Abstract The arithmetic correlations of two binary half‐ ℓ ‐sequences with connection integer p r , which is an odd prime power, are investigated. Possible values (of the arithmetic correlation) are calculated. In particular, if p ≡ 1 (mod 8), the authors prove that they are zero for non‐trivial shifts, that is, the half‐ ℓ ‐sequences have ideal arithmetic correlations. If p ≡ −1 (mod 8), an upper bound, which is of order of magnitude p r −1/2 ln p , is derived by using earlier results on the imbalance of half‐ ℓ ‐sequences with connection integer p studied by Gu and Klapper and later improved by Wang and Tan.

The (classical) crosscorrelation is an important measure of pseudorandomness of two binary sequences for applications in communications. The arithmetic crosscorrelation is another figure of merit introduced by Goresky and Klapper generalizing Mandelbaum’s arithmetic autocorrelation. First we observe that the arithmetic crosscorrelation is constant for two binary sequences of coprime periods, which complements the analogous result for the classical crosscorrelation. Then we prove upper bounds for the constant arithmetic crosscorrelation of two Legendre sequences of different periods and of two binary$m$-sequences of coprime periods, respectively.

It is well known that the computation of bilinear pairing is the most expensive operation in pairing-based cryptography. In this paper, we propose a noninteractive verifiable outsourcing algorithm of bilinear pairing based on two servers in the one-malicious model. The outsourcer need not execute any expensive operation, such as scalar multiplication and modular exponentiation. Moreover, the outsourcer could detect any failure with a probability close to 1 if one of the servers misbehaves. Therefore, the proposed algorithm improves checkability and decreases communication cost compared with the previous ones. Finally, we utilize the proposed algorithm as a subroutine to achieve an anonymous identity-based encryption (AIBE) scheme with outsourced decryption and an identity-based signature (IBS) scheme with outsourced verification.