An MPC framework for efficient navigation of mobile robots in cluttered environments

Abstract

We present a model predictive control (MPC) framework for efficient navigation of mobile robots in cluttered environments. The proposed approach integrates a finite-segment shortest path planner into the finite-horizon trajectory optimization of the MPC. This formulation ensures convergence to dynamically selected targets and guarantees collision avoidance, even under general nonlinear dynamics and cluttered environments. The approach is validated through hardware experiments on a small ground robot, where a human operator dynamically assigns target locations that a robot should reach while avoiding obstacles. The robot reached new targets within 2-3 seconds and responded to new commands within 50 ms to 100 ms, immediately adjusting its motion even while still moving at high speeds toward a previous target.

Figures (8)

• Figure 1: Visualization of the proposed control approach to navigate through cluttered environments. The MPC formulation jointly optimizes a short dynamic trajectory (blue) followed by a discrete path (green, purple) to reach the user-specified target (red circle), while avoiding obstacles (yellow).
• Figure 2: Illustration of a standard MPC for tracking limon2018nonlinearkrupa2024model (left) and the proposed formulation (right) in an environment obstructed by a challenging obstacle. Obstacles (orange) are surrounded by a buffer to account for robot geometry (light blue region). The mobile robot (blue) tries to reach the target (red circle). The MPC optimizes a trajectory (blue) to reach an artificial reference (green circle) and minimize an offset cost to the target. Left: The distance is directly minimized and the robot gets stuck in front of the obstacle. Right: The offset cost optimizes a 3-segment path (green, dashed) to the target and successfully navigates around the obstacle towards the target.
• Figure 3: Illustration of the shortest path road map with vehicle (blue), four obstacles (yellow), inflated obstacles (light blue region), and target (red). The roadmap is constructed from collision-free edges connecting vertices of inflated polytopic obstacles. The first and last segment connect the vehicle and the target to the graph and then remaining segments are the edges of the graph.
• Figure 4: Illustration of the intermediate target with obstacles (yellow), inflated obstacles (light blue), and target (red circle). Top: shortest path calculated from the start to the target. Bottom: The MPC optimizes over the predicted trajectory (blue, solid) and $n_\nu=3$ segments (green, dashed). The segments end at the pre-computed shortest path (purple), which is incremented whenever possible. Note that the optimized segments differ from the pre-computed shortest path.
• Figure 5: Visualization of exemplary randomly generated environments. Car and predicted trajectory (blue, solid), target (red circle), obstacles (yellow), inflated obstacles (light blue). Top: Sparse environment with $n_{\mathrm{o}}=6$ obstacles and MPC with the $L_2$-norm offset cost (green, dashed). Bottom: Dense environment with $n_{\mathrm{o}}=15$ obstacles and MPC with proposed segment-based offset cost, consisting of the optimized segmented (green, dashed), intermediate target $\hat{y}^{\mathrm{d}}_t$ (large green circle), and the remaining shortest path (purple, dotted). Since the $L_2$ formulation considers a straight line, the car would get stuck in front of the obstacle; while the proposed approach directly uses a collision-free path for navigation.

Theorems & Definitions (12)

• Remark 1: Terminal constraint
• Remark 2: Practical considerations
• Proposition 1
• Proposition 2
• Theorem 1
• Lemma 1
• Remark 3: Alternative global planners
• Theorem 2
• proof
• proof