The main objective of this research is the development of a framework for the automatic generation of systems of kinematic and dynamic equations that are suitable for real-time applications. In particular, the efficient simulation of constrained multibody systems is addressed. When modelled with ideal joints, many mechanical systems of practical interest contain closed kinematic chains, or kinematic loops, and are most conveniently modelled using a set of generalized coordinates of cardinality exceeding the degrees-of-freedom of the system. Dependent generalized coordinates add nonlinear algebraic constraint equations to the ordinary differential equations of motion, thereby producing a set of differential-algebraic equations that may be difficult to solve in an efficient yet precise manner. Several methods have been proposed for simulating such systems in real time, including index reduction, model simplification, and constraint stabilization techniques. In this work, the equations of motion are formulated symbolically using linear graph theory. The embedding technique is applied to eliminate the Lagrange multipliers from the dynamic equations and obtain one ordinary differential equation for each independent acceleration. The theory of Gröbner bases is then used to triangularize the kinematic constraint equations, thereby producing recursively solvable systems for calculating the dependent generalized coordinates given values of the independent coordinates. For systems that can be fully triangularized, the kinematic constraints are always satisfied exactly and in a fixed amount of time. Where full triangularization is not possible, a block-triangular form can be obtained that still results in more efficient simulations than existing iterative and constraint stabilization techniques. The proposed approach is applied to the kinematic and dynamic simulation of several mechanical systems, including six-bar mechanisms, parallel robots, and two vehicle suspensions: a five-link and a double-wishbone. The efficient kinematic solution generated for the latter is used in the real-time simulation of a vehicle with double-wishbone suspensions on both axles, which is implemented in a hardware- and operator-in-the-loop driving simulator. The Gröbner basis approach is particularly suitable for situations requiring very efficient simulations of multibody systems whose parameters are constant, such as the plant models in model-predictive control strategies and the vehicle models in driving simulators.

Electromyographic (EMG) signal decomposition is the process of resolving an EMG signal into its component motor unit potential trains (MUPTs). The extracted MUPTs can aid in the diagnosis of neuromuscular disorders and the study of the neural control of movement, but only if they are valid trains. Before using decomposition results and the motor unit potential (MUP) shape and motor unit (MU) firing pattern information related to each active MU for either clinical or research purposes the fact that the extracted MUPTs are valid needs to be confirmed. The existing MUPT validation methods are either time consuming or related to operator experience and skill. More importantly, they cannot be executed during automatic decomposition of EMG signals to assist with improving decomposition results. To overcome these issues, in this thesis the possibility of developing automatic MUPT validation algorithms has been explored. Several methods based on a combination of feature extraction techniques, cluster validation methods, supervised classification algorithms, and multiple classifier fusion techniques were developed. The developed methods, in general, use either the MU firing pattern or MUP-shape consistency of a MUPT, or both, to estimate its overall validity. The performance of the developed systems was evaluated using a variety of MUPTs obtained from the decomposition of several simulated and real intramuscular EMG signals. Based on the results achieved, the methods that use only shape or only firing pattern information had higher generalization error than the systems that use both types of information. For the classifiers that use MU firing pattern information of a MUPT to determine its validity, the accuracy for invalid trains decreases as the number of missed-classification errors in trains increases. Likewise, for the methods that use MUP-shape information of a MUPT to determine its validity, the classification accuracy for invalid trains decreases as the within-train similarity of the invalid trains increase. Of the systems that use both shape and firing pattern information, those that separately estimate MU firing pattern validity and MUP-shape validity and then estimate the overall validity of a train by fusing these two indices using trainable fusion methods performed better than the single classifier scheme that estimates MUPT validity using a single classifier, especially for the real data used. Overall, the multi-classifier constructed using trainable logistic regression to aggregate base classifier outputs had the best performance with overall accuracy of 99.4% and 98.8% for simulated and real data, respectively. The possibility of formulating an algorithm for automated editing MUPTs contaminated with a high number of false-classification errors (FCEs) during decomposition was also investigated. Ultimately, a robust method was developed for this purpose. Using a supervised classifier and MU firing pattern information provided by each MUPT, the developed algorithm first determines whether a given train is contaminated by a high number of FCEs and needs to be edited. For contaminated MUPTs, the method uses both MU firing pattern and MUP shape information to detect MUPs that were erroneously assigned to the train. Evaluation based on simulated and real MU firing patterns, shows that contaminated MUPTs could be detected with 84% and 81% accuracy for simulated and real data, respectively. For a given contaminated MUPT, the algorithm on average correctly classified around 92.1% of the MUPs of the MUPT. The effectiveness of using the developed MUPT validation systems and the MUPT editing methods during EMG signal decomposition was investigated by integrating these algorithms into a certainty-based EMG signal decomposition algorithm. Overall, the decomposition accuracy for 32 simulated and 30 real EMG signals was improved by 7.5% (from 86.7% to 94.2%) and 3.4% (from 95.7% to 99.1%), respectively. A significant improvement was also achieved in correctly estimating the number of MUPTs represented in a set of detected MUPs. The simulated and real EMG signals used were comprised of 3–11 and 3–15 MUPTs, respectively.

This thesis presents an approach to modelling dynamic mass capture which is applied to a number of system models. The models range from a simple 2D Euler-Bernoulli beam with point masses for the end-effector and target to a 3D Timoshenko beam model (including torsion) with rigid bodies for the end-effector and target. In addition, new models for torsion, as well as software to derive the finite element equations from first principles were developed to support the modelling. Results of the models are compared to a simple experiment as done by Ben Rhody. Investigations of offset capture are done by simulation to show why one would consider using a 3D model that includes torsion. These problems have relevance to both terrestrial robots and to space based robotic systems such as the manipulators on the International Space Station capturing payloads such as the SpaceX Dragon capsule. One could increase production in an industrial environment if industrial robots could pick up items without having to establish a zero relative velocity between the end effector and the item. To have a robot acquire its payload in this way would introduce system dynamics that could lead to the necessity of modelling a previously ‘rigid’ robot as flexible.