The ability of autonomous agents like Unmanned Aerial Vehicles (UAVs) and spaceships to avoid collision with static and dynamic obstacles while navigating through an obstacle-cluttered environment is very critical for overall success in any mission. Over the years, There have been significant efforts culminating into some well-established collision avoidance algorithms like Velocity Obstacle (VO), Optimally Reciprocal Collision Avoidance, Nonlinear Velocity Obstacle, Probabilistic Velocity Obstacle (PVO), Collision Cone, etc. to achieve collision avoidance. However, in their basic set-ups several of them assume constant velocity model for the obstacles and does not take into consideration the dynamic constraints of the agent. In the limited setting, when agent-obstacles are alike in terms of planning and control, collision avoiding methods like Acceleration Velocity Obstacle (AVO) do take into account the agent’s and obstacles’ dynamic constraints. Still they are not robust to sensor noise and environmental uncertainty. The increased involvement of UAVs in our day to day lives and the availability of once expensive, and ever-improving computational power, has necessitated an algorithm to be able to plan for safe dynamically constrained navigation in an environment with uncertainty in the motion of the obstacles, sensor noise and uncertainty beyond the occluded regions. To this end, as an expansion over the PVO and AVO methods, a novel motion planner-Indicator probabilistic Acceleration Velocity Obstacle (IPAVO) method-is developed in this paper for smooth, collision-free navigation of the agent with acceleration constraints in an uncertain, unstructured environments with an element of anticipation for the future environment. Effectiveness of the developed IPAVO algorithm for safe collision-free smooth navigation of the agent is investigated in simulation studies in two environments with obstacles having constant velocity aother with obstacles maneuvering on a trajectory. Then in a hybrid environment consisting of the linear motion obstacle and dynamic maneuvering obstacles, an Extensive simulation studies is performed to elucidate the performance of the proposed IPAVO algorithm on four crucial parameters-target interception time, computational cycle time, minimum obstacle distance, and overall control effort under variable obstacle density. The algorithm deftly handles the environmental uncertainty and with all these desired features, IPAVO has the potential of real-time implementation. © 2021, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved.