An Automatic Algorithm to Derive Linear Vector Form of Lagrangian Equation of Motion with Collision and Constraint

The use of complex systems with switching behavior and control design such as multitask walking and flying robots which need different Equation of Motion (EOM) for their states has become more popular recently. Having a reliable, exact and easy to drive dynamic model is important for their analysis, design, path planning and control. While the Newton and Lagrange approaches are being used widely to derive robot dynamics, they are not fully optimized for numerical modelling of systems with switching behaviors. TMT method which is a linear vector form for Lagrange EOM has recently been used, but not generally intruded and investigated, to simplify the EOM derivation and improve the numerical simulation efficiency of robotic system models. Here a systematic approach to derive EOM of different rigid body robot systems with impact using TMT method is presented. An automatic algorithm and a code based on that is developed in Matlab language to derive different systems’ EOM. The algorithm needs simple geometric inputs for joints, actuator inputs, external loadings and constraints; and can be used for modelling both serial and parallel mechanism with external collision. The application of this approach and algorithm inputs is shown for three sample systems: a biped walker with upper body, a flapping flyer and a Clemens joint.