## 1 Introduction  
Autonomous mobile robots can be widely used in complex multiple tasks such as exploration and patrol. In this work, we focus on the deployment of mobile robots in dynamic indoor environments, such as the home environment. When robots operate in real-world environments, particularly when they interact with humans, ensuring safety becomes a critical requirement [1, 2]. While end-to-end learning-based decision-making methods have demonstrated remarkable progress in recent years, they remain inferior to classical planning-based methods in terms of interpretability, robustness, and safety. The key is to predict the future trajectories of the surrounding traffic participants. Current autonomous driving systems treat prediction and planning as separate and sequential parts, and the prediction module is independent of the planning module. However, these two tasks are inherently interdependent: effective planning relies on informed predictions, and prediction outcomes can be influenced by the robot's intended actions. Another fundamental challenge is the formulation of an appropriate cost function that can simultaneously evaluate future motion plans and balance competing objectives--such as minimizing the risk of collision while maximizing navigation efficiency. Achieving this trade-off is crucial for robust, real-time decision-making in uncertain environments.  
When operating in environments that contain both dynamic and static obstacles, a robot must be capable of accurately identifying and characterizing each type. The motion of dynamic obstacles, including their direction and speed, often exhibits significant randomness and variability [3]. Many existing motion prediction systems rely on single-speed or fixed-pattern models, which fail to account for such fluctuations. As a result, these systems are often ineffective in scenarios involving variable-speed obstacles. This limitation restricts the robot's ability to formulate flexible and adaptive movement strategies, thereby reducing its effectiveness in navigating complex and dynamic environments.  
To address the aforementioned challenges in motion planning, this paper proposes a novel method that incorporates high- and low-speed prediction. First, accurate obstacle detection and data fusion are achieved through multi-sensor perception and classification techniques, enabling the development of a comprehensive dynamic environment perception system. Next, a high- and low-speed prediction framework is introduced using the K-GRU method, which effectively performs feature classification and trajectory prediction for both static and dynamic obstacles moving at varying speeds. Finally, path planning in complex dynamic environments is accomplished by integrating heuristic search algorithms with predictive motion optimization strategies, enabling efficient avoidance of previously unknown dynamic obstacles.  
In summary, the contributions of this work are as follows:  
(1) High-and low-speed obstacle prediction: A novel viewpoint-based method leveraging a spatiotemporal joint model is proposed to accurately predict dynamic obstacle trajectories across varying speeds in unstructured environments.  
(2) Adaptive motion planning optimization: An adaptive adjustment factor is integrated into the planning framework to dynamically tune parameters based on real-time obstacle information, enhancing dynamic obstacle avoidance and path optimality.  
(3) Validation and code release: The method achieves strong performance in both simulation and real-world tests. The source code is publicly available (Source code: [[https://github.com/lft1001/IMPP-AD.git](https://github.com/lft1001/IMPP-AD.git)]([https://github.com/lft1001/IMPP-AD.git](https://github.com/lft1001/IMPP-AD.git)), accessed on 14 May 2025).