PC-SNN: Supervised Learning with Local Hebbian Synaptic Plasticity based on Predictive Coding in Spiking Neural Networks

Deemed as the third generation of neural networks, the event-driven Spiking Neural Networks(SNNs) combined with bio-plausible local learning rules make it promising to build low-power, neuromorphic hardware for SNNs. However, because of the non-linearity and discrete property of spiking neural networks, the training of SNN remains difficult and is still under discussion. Originating from gradient descent, backprop has achieved stunning success in multi-layer SNNs. Nevertheless, it is assumed to lack biological plausibility, while consuming relatively high computational resources. In this paper, we propose a novel learning algorithm inspired by predictive coding theory and show that it can perform supervised learning fully autonomously and successfully as the backprop, utilizing only local Hebbian plasticity. Furthermore, this method achieves a favorable performance compared to the state-of-the-art multi-layer SNNs: test accuracy of 99.25% for the Caltech Face/Motorbike dataset, 84.25% for the ETH-80 dataset, 98.1% for the MNIST dataset and 98.5% for the neuromorphic dataset: N-MNIST. Furthermore, our work provides a new perspective on how supervised learning algorithms are directly implemented in spiking neural circuitry, which may give some new insights into neuromorphological calculation in neuroscience.Comment: 15 pages, 11fig

Multi-kernel Correntropy-based Orientation Estimation of IMUs: Gradient Descent Methods

This paper presents two computationally efficient algorithms for the orientation estimation of inertial measurement units (IMUs): the correntropy-based gradient descent (CGD) and the correntropy-based decoupled orientation estimation (CDOE). Traditional methods, such as gradient descent (GD) and decoupled orientation estimation (DOE), rely on the mean squared error (MSE) criterion, making them vulnerable to external acceleration and magnetic interference. To address this issue, we demonstrate that the multi-kernel correntropy loss (MKCL) is an optimal objective function for maximum likelihood estimation (MLE) when the noise follows a type of heavy-tailed distribution. In certain situations, the estimation error of the MKCL is bounded even in the presence of arbitrarily large outliers. By replacing the standard MSE cost function with MKCL, we develop the CGD and CDOE algorithms. We evaluate the effectiveness of our proposed methods by comparing them with existing algorithms in various situations. Experimental results indicate that our proposed methods (CGD and CDOE) outperform their conventional counterparts (GD and DOE), especially when faced with external acceleration and magnetic disturbances. Furthermore, the new algorithms demonstrate significantly lower computational complexity than Kalman filter-based approaches, making them suitable for applications with low-cost microprocessors

Multi-kernel Correntropy Regression: Robustness, Optimality, and Application on Magnetometer Calibration

This paper investigates the robustness and optimality of the multi-kernel correntropy (MKC) on linear regression. We first derive an upper error bound for a scalar regression problem in the presence of arbitrarily large outliers and reveal that the kernel bandwidth should be neither too small nor too big in the sense of the lowest upper error bound. Meanwhile, we find that the proposed MKC is related to a specific heavy-tail distribution, and the level of the heavy tail is controlled by the kernel bandwidth solely. Interestingly, this distribution becomes the Gaussian distribution when the bandwidth is set to be infinite, which allows one to tackle both Gaussian and non-Gaussian problems. We propose an expectation-maximization (EM) algorithm to estimate the parameter vectors and explore the kernel bandwidths alternatively. The results show that our algorithm is equivalent to the traditional linear regression under Gaussian noise and outperforms the conventional method under heavy-tailed noise. Both numerical simulations and experiments on a magnetometer calibration application verify the effectiveness of the proposed method

Generalized Multi-kernel Maximum Correntropy Kalman Filter for Disturbance Estimation

Disturbance observers have been attracting continuing research efforts and are widely used in many applications. Among them, the Kalman filter-based disturbance observer is an attractive one since it estimates both the state and the disturbance simultaneously, and is optimal for a linear system with Gaussian noises. Unfortunately, The noise in the disturbance channel typically exhibits a heavy-tailed distribution because the nominal disturbance dynamics usually do not align with the practical ones. To handle this issue, we propose a generalized multi-kernel maximum correntropy Kalman filter for disturbance estimation, which is less conservative by adopting different kernel bandwidths for different channels and exhibits excellent performance both with and without external disturbance. The convergence of the fixed point iteration and the complexity of the proposed algorithm are given. Simulations on a robotic manipulator reveal that the proposed algorithm is very efficient in disturbance estimation with moderate algorithm complexity.Comment: in IEEE Transactions on Automatic Control (2023

Randomized Optimal Design of Parallel Manipulators

This work intends to deal with the optimal kinematic synthesis problem of parallel manipulators under a unified framework. Observing that regular (e.g., hyper-rectangular) workspaces are desirable for most machines, we propose the concept of effective regular workspace, which reflects simultaneously requirements on the workspace shape and quality. The effectiveness of a workspace is characterized by the dexterity of the mechanism over every point in the workspace. Other performance indices, such as manipulability and stiffness, provide alternatives of dexterity characterization of workspace effectiveness. An optimal design problem, including constraints on actuated/passive joint limits and link interference, is then formulated to find the manipulator geometry that maximizes the effective regular workspace. This problem is a constrained nonlinear optimization problem without explicitly analytical expression. Traditional gradient based approaches may have difficulty in searching the global optimum. The controlled random search technique, as reported robust and reliable, is used to obtain an numerical solution. The design procedure is demonstrated through examples of a Delta robot and a Gough-Stewart platform. Note to Practitioners-The kinematic/dynamic performance of a parallel manipulator highly depends on its geometry, e.g., link lengths, positions of fixed actuator, shape and size of end-effector. In designing a parallel manipulator, it is a crucial step to determine the best geometry that satisfies practical design requirements. For a general parallel manipulator, this paper provides a unified framework to formulate the optimal design problem by considering some key kinematic criteria, regularity and volume of workspace and dexterity. The latter one is closely related to stiffness and control accuracy. Since the optimal design problem is a nonlinear optimization problem without analytic expression, traditional gradient based search algorithms have difficulty to solve the problem. The controlled random search technique is used to search the global optimum. The design procedure is applicable for general parallel manipulators. Other design criteria, such as stiffness and accuracy, can be readily included in the design formulation

Dynamic Object Tracking for Quadruped Manipulator with Spherical Image-Based Approach

Exactly estimating and tracking the motion of surrounding dynamic objects is one of important tasks for the autonomy of a quadruped manipulator. However, with only an onboard RGB camera, it is still a challenging work for a quadruped manipulator to track the motion of a dynamic object moving with unknown and changing velocities. To address this problem, this manuscript proposes a novel image-based visual servoing (IBVS) approach consisting of three elements: a spherical projection model, a robust super-twisting observer, and a model predictive controller (MPC). The spherical projection model decouples the visual error of the dynamic target into linear and angular ones. Then, with the presence of the visual error, the robustness of the observer is exploited to estimate the unknown and changing velocities of the dynamic target without depth estimation. Finally, the estimated velocity is fed into the model predictive controller (MPC) to generate joint torques for the quadruped manipulator to track the motion of the dynamical target. The proposed approach is validated through hardware experiments and the experimental results illustrate the approach's effectiveness in improving the autonomy of the quadruped manipulator

Optimal design of parallel manipulators

Parallel manipulators potentially possess some superior properties over their serial counterparts, e.g., high ratio of load to self weight, low inertia, high stiffness, etc. Differing greatly from that of a serial manipulator, however, the performance of a parallel manipulator highly depends on its dimensions. A dimensional syn-thesis is absolutely necessary to maintain advantages of a parallel manipulator and complying as close as possible with the performance needed for the task at hand. This work intends to deal with the optimal kinematic synthesis problem of parallel manipulators. A unified framework is novelly proposed for optimal de-sign of parallel manipulators. By observing that regular (e.g., hyperrectangular) workspaces are desirable for most machines, we propose the concept of effec-tive regular workspace, which reflects both requirements on the workspace shape and quality. Dexterity index is utilized to characterize the effectiveness of the workspace. Other performance indices, such as manipulability, stiffness, and minimal natural frequency, can be readily included. The optimal design problem is then formulated to find a manipulator geometry that maximizes the effective regular workspace. Since the optimal design problem is a multimodal constrained nonlinear optimization problem without explicit analytical expression, traditional gradient based optimization techniques may have difficulty in searching the global optimum. The controlled random search (CRS) technique, which was reported as a robust and reliable direct search method, is applied to numerically solve the problem. Some typical parallel manipulators, a five-bar parallel linkage, a rota-tional Delta robot, and a Gough-Stewart platform are employed as examples to demonstrate the design procedure. We prove rigorously that a fully parallel mechanism consisting of 3-P Pa* sub-chains undergoes generically 3-DoF purely translational motion. Here, Pa* rep-resents a spatial parallelogram whose joints are all spherical joints. Using the novelly proposed design formulation, a thorough search of all parallel mechanisms having a 3-P Pa* topology, is conducted. For mechanisms having 3-P Pa* topology, the best architecture is the one whose all prismatic joint axes are perpendicular mutually and intersect at a common point. We name this architecture Orthopod. This mechanism is simple in topology and easy for assembly. A prototype ma-chine is manufactured. Positioning control and velocity based trajectory tracking experiments are conducted. The prototype Orthopod shows good performance in positioning accuracy

Kinematics and optimal design of a novel 3-DoF parallel manipulator for pick-and-place applications

In this paper, a novel 3-degree-of-freedom planar parallel manipulator, the V3 robot, is introduced. The manipulator consists of three RRR (R: revolute joint) subchains, which are respectively arranged in three-parallel planes. The three-actuated joints are designed to have a common rotation axis, which contributes the large workspace and unlimited rotational capability of the robot. The kinematics, including the loop-closure equations, the inverse kinematics, singularity, and workspace are briefly analysed. By directly considering the velocity and the accuracy indices for pick and place operations, the optimal design problem is formulated to maximise the good performance workspace, where lower bounds on the average extreme velocity and upper bounds on the average extreme error are applied as constraints. The optimal design shows greatly improved performance in workspace, velocity, and accuracy

An integrated structure and control design of a coaxis planar parallel manipulator for pick-and-place applications based on elastic potential energy

During high-speed pick-and-place operations, elastic deformations are quite apparent if the mass of the manipulator is low. These irregular deformations are accompanied by vibrations, then errors. Since elastic potential energy reflects elastic deformation, the vibration of the whole manipulator can be controlled well when the elastic potential energy is decreased. In this article, to design manipulators with flexible links for pick-and-place operations, an integrated structure and control design framework is proposed. The dynamic model of a coaxis planar parallel manipulator is obtained by the finite element method, an effective method. A proportional–derivative controller is utilized for this industrial application. Simultaneously, the optimal structural and control parameters are derived by minimizing the elastic potential energy via integrated design, in which actuated systems and accuracies are regarded as constraints. Finally, simulations show that the performance of the parallel manipulator is improved by this design methodology