Non-Conservative Efficient Collision Checking and Depth Noise-Awareness for Trajectory Planning

This paper presents <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MIDI</b> (<bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</b>inimum d<bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</b>stance-based and <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</b>epth-no<bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</b>se-aware), a novel trajectory planner that introduces non-conservative collision checking and depth noise awareness for robust autonomous navigation. Unlike existing collision-checking approaches that rely on trajectory discretization or geometric approximations of free space, MIDI evaluates each depth pixel independently against an entire trajectory at once. Thus, it bypasses both the notorious grid-size problem in trajectory discretization and conservativeness inherent in free space geometric approximations. Leveraging polynomial trajectory properties to compute minimum distances and collision probabilities for all obstacle points in closed-form, MIDI facilitates both non-conservative and real-time trajectory collision checking. Moreover, to the best of our knowledge, MIDI is the first memoryless planner that explicitly incorporates depth uncertainty information into online trajectory planning. Extensive simulations show that MIDI outperforms state-of-the-art memoryless planners, maintaining robust performance even under severe depth noise, where competing methods show significant degradation. The algorithm's non-conservative nature enables better utilization of free space, resulting in notably lower incompletion rates in cluttered environments. Finally, real-world flight trials were conducted to validate the effectiveness of our approach in an actual quadrotor.