Virtual Dental Articulation Using Computed Tomography Data and Motion Tracking

Dental articulation holds crucial and fundamental importance in the design of dental restorations and analysis of prosthetic or orthodontic occlusions. However, common traditional and digital articulators are difficult and cumbersome in use to effectively translate the dental cast model to the articulator workspace when using traditional facebows. In this study, we have developed a personalized virtual dental articulator that directly utilizes computed tomography (CT) data to mathematically model the complex jaw movement, providing a more efficient and accurate way of analyzing and designing dental restorations. By utilizing CT data, Frankfurt's horizontal plane was established for the mathematical modeling of virtual articulation, eliminating tedious facebow transfers. After capturing the patients' CT images and tracking their jaw movements prior to dental treatment, the jaw-tracking information was incorporated into the articulation mathematical model. The validation and analysis of the personalized articulation approach were conducted by comparing the jaw movement between simulation data (virtual articulator) and real measurement data. As a result, the proposed virtual articulator achieves two important functions. Firstly, it replaces the traditional facebow transfer process by transferring the digital dental model to the virtual articulator through the anatomical relationship derived from the cranial CT data. Secondly, the jaw movement trajectory provided by optical tracking was incorporated into the mathematical articulation model to create a personalized virtual articulation with a small Fréchet distance of 1.7 mm. This virtual articulator provides a valuable tool that enables dentists to obtain diagnostic information about the temporomandibular joint (TMJ) and configure personalized settings of occlusal analysis for patients.

A Comprehensive Review of Vision-Based Robotic Applications: Current State, Components, Approaches, Barriers, and Potential Solutions

Being an emerging technology, robotic manipulation has encountered tremendous advancements due to technological developments starting from using sensors to artificial intelligence. Over the decades, robotic manipulation has advanced in terms of the versatility and flexibility of mobile robot platforms. Thus, robots are now capable of interacting with the world around them. To interact with the real world, robots require various sensory inputs from their surroundings, and the use of vision is rapidly increasing nowadays, as vision is unquestionably a rich source of information for a robotic system. In recent years, robotic manipulators have made significant progress towards achieving human-like abilities. There is still a large gap between human and robot dexterity, especially when it comes to executing complex and long-lasting manipulations. This paper comprehensively investigates the state-of-the-art development of vision-based robotic application, which includes the current state, components, and approaches used along with the algorithms with respect to the control and application of robots. Furthermore, a comprehensive analysis of those vision-based applied algorithms, their effectiveness, and their complexity has been enlightened here. To conclude, there is a discussion over the constraints while performing the research and potential solutions to develop a robust and accurate vision-based robot manipulation.

Comparative analysis of inverse kinematics methodologies to improve the controllability of rehabilitative robotic devices

The solution of the inverse kinematics problem in multi-degrees of freedom robots has been tackled, through the last three decades, by several different approaches including analytical, geometrical, differential and numerical methods. All these techniques present their own advantages and drawbacks. However, a guideline on which approach is better to follow, depending on the kind of task to perform and the type of robotic device used, is still missing. In this work, a quantitative comparative analysis of three different inverse kinematics methodologies for the control of rehabilitative robotic devices is proposed, with aim of devising best practices and guidelines for the selection of the most suitable approach. The analyzed methodologies are implemented and numerically tested on two actual devices, specifically an upper-limb exoskeleton and an upper-limb prosthetic arm.

Offline motion libraries and online MPC for advanced mobility skills

We describe an optimization-based framework to perform complex locomotion skills for robots with legs and wheels. The generation of complex motions over a long-time horizon often requires offline computation due to current computing constraints and is mostly accomplished through trajectory optimization (TO). In contrast, model predictive control (MPC) focuses on the online computation of trajectories, robust even in the presence of uncertainty, albeit mostly over shorter time horizons and is prone to generating nonoptimal solutions over the horizon of the task’s goals. Our article’s contributions overcome this trade-off by combining offline motion libraries and online MPC, uniting a complex, long-time horizon plan with reactive, short-time horizon solutions. We start from offline trajectories that can be, for example, generated by TO or sampling-based methods. Also, multiple offline trajectories can be composed out of a motion library into a single maneuver. We then use these offline trajectories as the cost for the online MPC, allowing us to smoothly blend between multiple composed motions even in the presence of discontinuous transitions. The MPC optimizes from the measured state, resulting in feedback control, which robustifies the task’s execution by reacting to disturbances and looking ahead at the offline trajectory. With our contribution, motion designers can choose their favorite method to iterate over behavior designs offline without tuning robot experiments, enabling them to author new behaviors rapidly. Our experiments demonstrate complex and dynamic motions on our traditional quadrupedal robot ANYmal and its roller-walking version. Moreover, the article’s findings contribute to evaluating five planning algorithms.

Modern Machine Learning for Tackling Inverse Problems in Chemistry: Molecular Design to Realization

The discovery of new molecules and materials helps expand the horizons of novel and innovative real-life applications. In the pursuit of finding molecules with desired properties, chemists have traditionally relied...

Sensorimotor Self-organization via Circular-Reactions

Newborns demonstrate innate abilities in coordinating their sensory and motor systems through reflexes. One notable characteristic is circular reactions consisting of self-generated motor actions that lead to correlated sensory and motor activities. This paper describes a model for goal-directed reaching based on circular reactions and exocentric reference-frames. The model is built using physiologically plausible visual processing modules and arm-control neural networks. The model incorporates map representations with ego- and exo-centric reference frames for sensory inputs, vector representations for motor systems, as well as local associative learning that result from arm explorations. The integration of these modules is simulated and tested in a three-dimensional spatial environment using Unity3D. The results show that, through self-generated activities, the model self-organizes to generate accurate arm movements that are tolerant with respect to various sources of noise.

An Algorithm for Solving Robot Inverse Kinematics Based on FOA Optimized BP Neural Network

The solution of robot inverse kinematics has a direct impact on the control accuracy of the robot. Conventional inverse kinematics solution methods, such as numerical solution, algebraic solution, and geometric solution, have insufficient solution speed and solution accuracy, and the solution process is complicated. Due to the mapping ability of the neural network, the use of neural networks to solve robot inverse kinematics problems has attracted widespread attention. However, it has slow convergence speed and low accuracy. This paper proposes the FOA optimized BP neural network algorithm to solve inverse kinematics. It overcomes the shortcomings of low convergence accuracy, slow convergence speed, and easy to fall into local minima when using BP neural network to solve inverse kinematics. The experimental results show that using the trained FOA optimized BP neural network to solve the inverse kinematics, the maximum error range of the output joint angle is [−0.04686, 0.1271]. The output error of the FOA optimized BP neural network algorithm is smaller than that of the ordinary BP neural network algorithm and the PSO optimized BP neural network algorithm. Using the FOA optimized BP neural network algorithm to solve the robot kinematics can improve the control accuracy of the robot.

Kinematic of the Position and Orientation Synchronization of the Posture of a n DoF Upper-Limb Exoskeleton with a Virtual Object in an Immersive Virtual Reality Environment

Exoskeletons are an external structural mechanism with joints and links that work in tandem with the user, which increases, reinforces, or restores human performance. Virtual Reality can be used to produce environments, in which the intensity of practice and feedback on performance can be manipulated to provide tailored motor training. Will it be possible to combine both technologies and have them synchronized to reach better performance? This paper consists of the kinematics analysis for the position and orientation synchronization between an n DoF upper-limb exoskeleton pose and a projected object in an immersive virtual reality environment using a VR headset. To achieve this goal, the exoskeletal mechanism is analyzed using Euler angles and the Pieper technique to obtain the equations that lead to its orientation, forward, and inverse kinematic models. This paper extends the author’s previous work by using an early stage upper-limb exoskeleton prototype for the synchronization process.

First return, then explore

Reinforcement learning promises to solve complex sequential-decision problems autonomously by specifying a high-level reward function only. However, reinforcement learning algorithms struggle when, as is often the case, simple and intuitive rewards provide sparse¹ and deceptive² feedback. Avoiding these pitfalls requires a thorough exploration of the environment, but creating algorithms that can do so remains one of the central challenges of the field. Here we hypothesize that the main impediment to effective exploration originates from algorithms forgetting how to reach previously visited states (detachment) and failing to first return to a state before exploring from it (derailment). We introduce Go-Explore, a family of algorithms that addresses these two challenges directly through the simple principles of explicitly 'remembering' promising states and returning to such states before intentionally exploring. Go-Explore solves all previously unsolved Atari games and surpasses the state of the art on all hard-exploration games¹, with orders-of-magnitude improvements on the grand challenges of Montezuma's Revenge and Pitfall. We also demonstrate the practical potential of Go-Explore on a sparse-reward pick-and-place robotics task. Additionally, we show that adding a goal-conditioned policy can further improve Go-Explore's exploration efficiency and enable it to handle stochasticity throughout training. The substantial performance gains from Go-Explore suggest that the simple principles of remembering states, returning to them, and exploring from them are a powerful and general approach to exploration-an insight that may prove critical to the creation of truly intelligent learning agents.

Model-Based Real-Time Motion Tracking Using Dynamical Inverse Kinematics

This paper contributes towards the development of motion tracking algorithms for time-critical applications, proposing an infrastructure for dynamically solving the inverse kinematics of highly articulate systems such as humans. The method presented is model-based, it makes use of velocity correction and differential kinematics integration in order to compute the system configuration. The convergence of the model towards the measurements is proved using Lyapunov analysis. An experimental scenario, where the motion of a human subject is tracked in static and dynamic configurations, is used to validate the inverse kinematics method performance on human and humanoid models. Moreover, the method is tested on a human-humanoid retargeting scenario, verifying the usability of the computed solution in real-time robotics applications. Our approach is evaluated both in terms of accuracy and computational load, and compared to iterative optimization algorithms.

Robust and efficient forward, differential, and inverse kinematics using dual quaternions

Modern approaches for robot kinematics employ the product of exponentials formulation, represented using homogeneous transformation matrices. Quaternions over dual numbers are an established alternative representation; however, their use presents certain challenges: the dual quaternion exponential and logarithm contain a zero-angle singularity, and many common operations are less efficient using dual quaternions than with matrices. We present a new derivation of the dual quaternion exponential and logarithm that removes the singularity, we show an implicit representation of dual quaternions offers analytical and empirical efficiency advantages compared with both matrices and explicit dual quaternions, and we derive efficient dual quaternion forms of differential and inverse position kinematics. Analytically, implicit dual quaternions are more compact and require fewer arithmetic instructions for common operations, including chaining and exponentials. Empirically, we demonstrate a 30–40% speedup on forward kinematics and a 300–500% speedup on inverse position kinematics. This work relates dual quaternions with modern exponential coordinates and demonstrates that dual quaternions are a robust and efficient representation for robot kinematics.

A General Approach Based on Newton’s Method and Cyclic Coordinate Descent Method for Solving the Inverse Kinematics

The inverse kinematics of robot manipulators is a crucial problem with respect to automatically controlling robots. In this work, a Newton-improved cyclic coordinate descent (NICCD) method is proposed, which is suitable for robots with revolute or prismatic joints with degrees of freedom of any arbitrary number. Firstly, the inverse kinematics problem is transformed into the objective function optimization problem, which is based on the least-squares form of the angle error and the position error expressed by the product-of-exponentials formula. Thereafter, the optimization problem is solved by combining Newton’s method with the improved cyclic coordinate descent (ICCD) method. The difference between the proposed ICCD method and the traditional cyclic coordinate descent method is that consecutive prismatic joints and consecutive parallel revolute joints are treated as a whole in the former for the purposes of optimization. The ICCD algorithm has a convenient iterative formula for these two cases. In order to illustrate the performance of the NICCD method, its simulation results are compared with the well-known Newton–Raphson method using six different robot manipulators. The results suggest that, overall, the NICCD method is effective, accurate, robust, and generalizable. Moreover, it has advantages for the inverse kinematics calculations of continuous trajectories.

Efficient Closed-Form Task Space Manipulability for a 7-DOF Serial Robot

With the increasing demand for robots to react and adapt to unforeseen events, it is essential that a robot preserves agility at all times. While manipulability is a common measure to quantify agility at a given joint configuration, an efficient direct evaluation in task space is usually not possible with conventional methods, especially for redundant robots with an infinite number of Inverse Kinematic solutions. Yet, this is essential for global online optimization of a robot posture. In this work, we derive analytical expressions for a conventional 7-degrees of freedom (7-DOF) serial robot structure, which enable the direct evaluation of manipulability from a reduced task space parametrization. The resulting expressions allow array operation and thus achieve very high computational efficiency with vector-optimized programming languages. This direct and simultaneous calculation of the task space manipulability for large numbers of poses benefits many optimization problems in robotic applications. We show applications in global optimization of robot mounting poses, as well as redundancy resolution with global online optimization w.r.t. manipulability.

Modeling Parallel Robot Kinematics for 3T2R and 3T3R Tasks Using Reciprocal Sets of Euler Angles

Industrial manipulators and parallel robots are often used for tasks, such as drilling or milling, that require three translational, but only two rotational degrees of freedom (“3T2R”). While kinematic models for specific mechanisms for these tasks exist, a general kinematic model for parallel robots is still missing. This paper presents the definition of the rotational component of kinematic constraints equations for parallel robots based on two reciprocal sets of Euler angles for the end-effector orientation and the orientation residual. The method allows completely removing the redundant coordinate in 3T2R tasks and to solve the inverse kinematics for general serial and parallel robots with the gradient descent algorithm. The functional redundancy of robots with full mobility is exploited using nullspace projection.

A method for the automatic generation of inverse kinematic maps in modular robotic systems

Flexible manufacturing based on rapidly reconfigurable robotic systems will enable factories to meet time-sensitive and fast-changing industrial demands. However, with the rise of modular systems there is also the need to quickly and easily determine which configuration is optimal for performing a certain task. In this article, we present a path-based ad hoc technique for determining the inverse and forward kinematics map based on relative joint space variable to reduce the computational complexity. The proposed technique is nonsingular and suits kinematic analysis and optimization of robotic systems with undetermined configuration, and it can be extended to solve generalized inverse kinematic of robotics system involving large number of joint variable.

A Fast Algorithm for Inverse Kinematic Analysis of Robot Manipulators

To solve the inverse kinematics problem, we obtain with little effort a reduced and complete set of equations by a conve nient choice of end-effector frame and application of rotation orthogonality. This approach does not require computation of the forward kinematics and can be used with manipulators of any geometry, although it is most efficient when applied to orthogonal manipulators, a class of robot arms defined in this paper. For manipulators requiring numerical techniques, but for which knowledge of one joint variable allows closed- form solutions of the remaining joint variables, an iterative inverse kinematic method, simple and fast enough to be suitable for real-time manipulator control, has been devel oped. The concepts and techniques presented in this paper are illustrated with two examples. The iterative method devel oped here performs a kinematic inversion of a 6-degree-of- freedom manipulator with no closed-form solutions in less than 30 ms using a desktop computer, an order of magnitude faster than times found in the literature.

Inverse kinematics solution of a new circumferential drilling machine for aircraft assembly

Inverse kinematics solutions are the basis for position and orientation control of automated machines in their Cartesian workspace. This paper presents an efficient and robust inverse kinematics algorithm for a new circumferential drilling machine for aircraft fuselage assembly. After a brief introduction to the circumferential drilling machine and its forward kinematics, the paper discusses the nonlinear optimization method for solving inverse kinematics problems. The objective function is defined as a weighted combination of a position error function and an orientation error function. By representing orientation error as the geodesic distance between two points on a unit sphere, the paper proposes to define the orientation error function by using faithful geodesic distance functions, which are accurate approximations to the geodesic distance when it is small. For increased efficiency, robustness, and easy setting of initial values, the inverse kinematics problem is decomposed into two subproblems. The revolute joint coordinates are obtained by nonlinear optimization, and the prismatic joint coordinates are calculated with closed-form formulas. Numerical experiments show that the objective function defined with faithful geodesic distance functions is effective, and the proposed algorithm is efficient, robust, and accurate. The algorithm has been successfully integrated into the control system of the circumferential drilling machine. Preliminary drilling experiments show that the position accuracy of drilled holes is within ±0.5 mm, which is acceptable for the assembly of large aircrafts.

Computational Development of Jacobian Matrices for Complex Spatial Manipulators

Current methods for developing manipulator Jacobian matrices are based on traditional kinematic descriptions such as Denavit and Hartenberg parameters. The resulting symbolic equations for these matrices become cumbersome and computationally inefficient when dealing with more complex spatial manipulators, such as those seen in the field of biomechanics. This paper develops a modified method for Jacobian development based on generalized kinematic equations that incorporates partial derivatives of matrices with Leibniz's Law (the product rule). It is shown that a set of symbolic matrix functions can be derived that improve computational efficiency when used in MATLAB(®) M-Files and are applicable to any spatial manipulator. An articulated arm subassembly and a musculoskeletal model of the hand are used as examples.

An adaptive niching genetic algorithm approach for generating multiple solutions of serial manipulator inverse kinematics with applications to modular robots

Inverse kinematics (IK) is a nonlinear problem that may have multiple solutions. A modified genetic algorithm (GA) for solving the IK of a serial robotic manipulator is presented. The algorithm is capable of finding multiple solutions of the IK through niching methods. Despite the fact that the number and position of solutions in the search space depends on the position and orientation of the end-effector as well as the kinematic configuration (KC) of the robot, the number of GA parameters that must be set by a user are limited to a minimum through the use of an adaptive niching method. The only requirement of the algorithm is the forward kinematics (FK) equations which can be easily obtained from the Denavit–Hartenberg link parameters and joint variables of the robot. For identifying and processing the outputs of the proposed GA, a modified filtering and clustering phase is also added to the algorithm. For the postprocessing stage, a numerical IK solver is used to achieve convergence to the desired accuracy. The algorithm is validated on three KCs of a modular and reconfigurable robot (MRR).

On a human-arm-like mechanical manipulator

This paper investigates the kinematics and motion of a human arm as a manipulator with seven degrees of freedom, and how to deal with the extra degree of freedom that exists. It proposes that a change of configuration be divided into a sequence of motions where each time one of the joints is locked. It then presents a general technique to solve inverse kinematic equations of the different reduced models that arise.

Task dependent synthesis of some geometrical parameters of a robot mechanism

This paper deals with the synthesis of a robot mechanism, which has an open kinematic chain structure. The aim of the synthesis is to find optimal mechanism link lengths and the elevation of the robot mechanism base, with respect to the arbitrary chosen task which is described in a task space.

A mathematical model, which describes the problem and enables one to use a nonlinear optimization algorithm, was developed. The usefulness of the approach is demonstrated by the example of the Manutec r3 mechanism with a prescribed task for the robot's end-effector.

A closed-loop inverse kinematic scheme for on-line joint-based robot control

A computationally fast inverse kinematic scheme is derived which solves robot's end-effector (EE) trajectories in terms of joint trajectories. The inverse kinematic problem (IKP) is cast as a control problem for a simple dynamic system. The resulting closed-loop algorithms are shown to guarantee satisfactory tracking performance. Differently from previous first-order schemes which only solve for joint positions and velocities, we propose here new second order tracking schemes which allow the on-line generation of joint position + velocity + acceleration (PVA) reference trajectories for any computed torque-like controller in sensor-based robot applications. The algorithms do explicitly solve the IKP for both EE position and orientation. Simulation results for a six-degree-of-freedom PUMA-like geometry demonstrate the effectiveness of the scheme, even near singularities.

Automated inverse-kinematics for robot off-line programming

Automated methods are developed to classify a robot's kinematic type and select an appropriate library inverse-kinematic solution based on this classification. These methods automatically generate DenavitHartenberg joint frame parameters, given any frame representation that can mathematically be represented as a homogeneous transformation.

To reduce the number of closed-form inverse-kinematics solutions required for a broad class of serial robots, additional methods account for differences in robot zero state, base frame location, and joint polarity. Further generalization results from using joint frame decoupling to map lower degree-of-freedom robots into the inverse-kinematics solutions of higher degree-offreedom robots.

Joint velocity uniformity in redundant robot manipulators

A redundant robot manipulator has several certain or expected advantages over a nonredundant one. It is expected, among other capabilities, that the joints vary with constant velocities during the execution of those tasks which in a nonredundant manipulator require variable joint velocities. In this way, motion becomes more precise because of the elimination of errors associated with velocity change in joints. In this paper, it is shown that this expected advantage is not possible for all the joints, and that only as many joints as the degree of redundancy can have constant velocities.