Simulation Model of a Mobile Robot’s Motion on a Support Surface with a Complex Profile

Background. Mobile robots (MRs) used in hard-to-reach or hazardous environments must possess high-profile maneuverability, which, due to their small chassis size, necessitates additional actuators to adjust the geometric parameters of the propulsion system and, consequently, complex motion control systems. Existing software packages for simulating the dynamics of rigid body systems do not always allow for accurate modeling of the interaction between the propulsion system (wheels) and a support surface with a complex profile, especially in cases involving multiple contact points. This complicates the development of effective control algorithms. Therefore, achieving the goal of this study—developing a simulation model of MR motion that combines modern software tools for mathematical modeling of rigid body dynamics with a wheel-terrain contact detection algorithm based on a modified GJK algorithm—is highly relevant. This approach will enable the study of MRs overcoming obstacles with complex profiles in near real-time conditions. Methods. The proposed approach for resolving the contact interaction between the propulsion system and uneven terrain is based on the GJK algorithm for detecting intersections between a wheel (represented as a truncated sphere) and the support surface profile (a set of convex polyhedrons). Based on the data obtained from the algorithm, contact forces and moments describing the interaction between the tire and the support surface are determined, accounting for its viscoelastic and adhesive properties. Results. A mathematical model of wheel interaction with uneven support surfaces in cases involving multiple contact points is proposed. This model is based on a modified GJK algorithm and enables the detection of contacts and interaction forces during MR motion simulation in near "real-time" conditions. The article evaluates the model’s performance and suitability for developing automatic MR motion control algorithms, using the example of a six-wheeled mobile robot overcoming a step obstacle. Conclusion. The developed model effectively studies MR motion when overcoming large obstacles and uneven terrain in cases with multiple contact points between the propulsion system and the support surface. The results confirm the model’s applicability and the potential of simulation-based mathematical modeling for synthesizing MR motion control laws.