Decentralized MPC based Obstacle Avoidance for Multi-Robot Target Tracking Scenarios

Abstract

In this work, we consider the problem of decentralized multi-robot target tracking and obstacle avoidance in dynamic environments. Each robot executes a local motion planning algorithm which is based on model predictive control (MPC). The planner is designed as a quadratic program, subject to constraints on robot dynamics and obstacle avoidance. Repulsive potential field functions are employed to avoid obstacles. The novelty of our approach lies in embedding these nonlinear potential field functions as constraints within a convex optimization framework. Our method convexifies non-convex constraints and dependencies, by replacing them as pre-computed external input forces in robot dynamics. The proposed algorithm additionally incorporates different methods to avoid field local minima problems associated with using potential field functions in planning. The motion planner does not enforce predefined trajectories or any formation geometry on the robots and is a comprehensive solution for cooperative obstacle avoidance in the context of multi-robot target tracking. Video of simulation studies: https://youtu.be/umkdm82Tt0M arXiv:1805.09633v1 [cs.RO]

Active Perception Based Formation Control for Multiple Aerial Vehicles

“…Motivated by multi-view cinematography applications, distributed non-linear model predictive control [14] is used to identify locally optimal motion plans for aerial vehicles. In one of our previous works [15], we developed a convex optimization program to generate local collision-free motion plans, while tracking a movable pick and place static target using multiple aerial vehicles. This approach generates fast, feasible motion plans and has a linear computational complexity (O(n)) in the number of environmental obstacles.…”

“…The factor |r des − x k t (n) − x P t 2 | in (10) helps avoid field local minima. This is because, if two robots have similar angles of approach (i.e., small d act (n)), the MAV farther away from the desired distance (r des ) is repelled with a higher force than the MAV near the desired distance (see [15] for a detailed explanation on how these forces avoid field local-minima problems associated with potential field based planners). Factor c is a small positive constant which ensures that the force magnitude is non-zero at the target surface if the desired angular difference is not yet achieved.…”

“…An external control input f k target (n) is computed so as to enforce her/his safety. Further, multiple static obstacles placed closed together might cause the MAV k to get stuck in a field local minima (as shown in [15]). To avoid these scenarios, we compute a force f k ang (n) to penalize MAV approach angles (γ k t (n)) which have static obstacles in the line of approach.…”

Motion Planning for Multi-Mobile-Manipulator Payload Transport Systems

“…This operation preserves the convexity of optimization. Incorporating external control inputs to avoid collisions within an MPC framework was presented in our previous work [19]. The repulsive potential field magnitude w.r.t the i th obstacle, is given as,…”

“…Approach Angle Force: Repulsive potential fields are used to deviate the DVB away from obstacles which lie along the direction of approach to the target. From (6), we utilize We term this external control input as approach angle force (introduced in [19]). The total obstacle avoidance external control input on B is given by,…”