Collision and obstacle avoidance for agents based on velocity programming in unknown environments under kinematical constraints

Abstract

Abstract This paper conducts research on obstacle and collision avoidance under kinematical constraints in unknown environments, while communication and simultaneous localization and mapping (SLAM) are unavailable to agents. Then a strategy based on mixed‐integer programming is proposed, in which velocity constraints are established with a modified Barrier function for obstacles that can be completely detected. As for obstacles that cannot be completely detected, a feasible set is built for the velocity programming based on the convex theory, and the contradicted constraints are addressed with the logic metric method. Besides, the actuator saturation is avoided by converting kinematical constraints into the restrictions on the magnitude, the restrictions on the direction, and the negative correlations between the components of the velocity respectively. Given that invalid nominal velocity leads to collisions, a virtual goal is estimated for nominal velocity improvement. In addition, the local extremum brought by empty programming space due to multiple constraints is repaired by fixing the velocity constraints. The feasibility of the proposed strategy is analyzed, and numerical simulations are provided to verify the effectiveness of the proposed strategy.

Keywords

• collision avoidance
• concave programming
• constraint satisfaction problems
• convex programming
• dynamic programming
• integer programming