SUMMARYAn analytical model with coupled dynamics for a realistic six-legged robotic system locomoting on various terrains has been developed, and its effectiveness has been proven through computer simulations and validated using virtual prototyping tools and real experiment. The approach is new and has not been attempted before. This study investigated the optimal feet-forces’ distributions under body force and foot–ground interaction considering compliant contact and friction force models for the feet undergoing slip. The kinematic model with 114 implicit constraints in 3D Cartesian space has been transformed in terms of generalized coordinates with a reduced explicit set of 24 constrained equations using kinematic transformations. The nonlinear constrained inverse dynamics model of the system has been formulated as a coupled dynamical problem using Newton–Euler method with realistic environmental conditions (compliant foot–ground contact, impact, and friction) and computed using optimization techniques due to its indeterminate nature. One case study has been carried out to validate the analytical data with the simulated ones executed in MSC.ADAMS® (Automated Dynamic Analysis of Mechanical Systems), while the other case study has been conducted to validate the analytical and simulated data with the experimental ones. In both these cases, results are found to be in close agreement, which proves the efficacy of the model.
On Constrained Equations with Singular Diffusivity