pith. sign in

arxiv: 2604.07599 · v2 · submitted 2026-04-08 · 💻 cs.RO

SANDO: Safe Autonomous Trajectory Planning for Dynamic Unknown Environments

Kota Kondo , Jes\'us Tordesillas , Jonathan P. How This is my paper

Pith reviewed 2026-05-10 16:57 UTC · model grok-4.3

classification 💻 cs.RO
keywords trajectory planningdynamic unknown environmentssafe flight corridorsMIQP optimizationUAV navigationcollision avoidanceformal safety analysisspatiotemporal planning
0
0 comments X

The pith

SANDO generates collision-free trajectories in unknown dynamic 3D environments by steering paths with risk heat maps and enforcing hard avoidance via time-specific obstacle corridors in a reduced MIQP.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces SANDO to plan safe paths for UAVs when obstacle locations and velocities are unknown ahead of time and can change at any moment. A heat-map A* global planner first avoids high-risk areas using soft costs, then a generator builds spatiotemporal safe flight corridors as time-layered polytopes that expand each obstacle only by its worst-case reachable set at that exact time layer. Trajectory optimization solves a mixed-integer quadratic program with hard collision constraints, sped up by eliminating variables, while formal analysis proves no collisions under explicit bounds on obstacle speeds and sensing errors. Ablation tests confirm the corridors are essential for feasibility in dense settings and that variable elimination yields major speed gains. Benchmarks and onboard flights show higher success rates than prior methods with zero violations even when using only perception data.

Core claim

SANDO produces safe trajectories by first using a heat map-based A* to guide the global path away from high-risk regions, then generating spatiotemporal safe flight corridors consisting of time-layered polytopes that inflate obstacles solely by their reachable sets at each time step rather than over the full horizon, and finally optimizing the trajectory as an MIQP that incorporates hard collision-avoidance constraints with a variable-elimination technique to enable rapid solving, all supported by formal safety guarantees under bounded-velocity and bounded-error assumptions.

What carries the argument

The spatiotemporal safe flight corridor (STSFC) generator, which builds time-layered polytopes using per-time worst-case reachable sets of obstacles to supply hard constraints to an MIQP solver whose variable count is reduced by elimination.

If this is right

  • SANDO achieves the highest success rate with no constraint violations across static, forest, and dynamic benchmarks at all difficulty levels.
  • Variable elimination reduces optimization time by up to 7.4 times while STSFCs maintain feasibility in dense dynamic environments.
  • Perception-only operation without ground-truth obstacle data still delivers robust performance under realistic sensing.
  • Formal analysis guarantees collision-free paths given explicit velocity bounds and estimation-error limits.
  • Hardware tests confirm ten safe flights among dynamic obstacles with fully onboard planning, perception, and localization.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Separating soft risk costs in global planning from hard constraints in local optimization may resolve the classic speed-safety trade-off for replanning tasks.
  • The time-layer approach to corridor inflation could reduce unnecessary conservatism compared with horizon-wide inflation in other dynamic planners.
  • Similar corridor and elimination techniques might transfer to ground robots or multi-agent coordination facing bounded but uncertain motions.
  • Tighter integration with learned obstacle predictors could relax the velocity-bound assumption while preserving the formal guarantees.

Load-bearing premise

Obstacles move with unknown but bounded velocities whose worst-case reachable sets can be computed accurately at each time layer without introducing hidden collisions or infeasibility.

What would settle it

A recorded collision occurring when an obstacle's actual velocity exceeds the bound used to compute its reachable set in the corridors, despite the planner completing without violations.

Figures

Figures reproduced from arXiv: 2604.07599 by Jes\'us Tordesillas, Jonathan P. How, Kota Kondo.

Figure 1
Figure 1. Figure 1: Comparison of trajectory planning approaches near a dynamic [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: SANDO system overview: Point cloud data are processed by the Map Manager, which detects static obstacles (denoted [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Unknown-space inflation for STSFC corridor generation. Boundary [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: STSFC corridors and MIQP trajectory optimization in dynamic environments. For visualization, the figure shows a 2D ( [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Visualization of the heat map-based global planner in hardware. [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Standardized Benchmarking: The environment used for benchmark [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Static Benchmarking: The static forest Gazebo environment used [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Rviz Visualization of Static Benchmarking (Hard Environment): [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Dynamic Benchmarking: The dynamic Gazebo environment used [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: Holybro PX4 Development Kit X500 is equipped with a Pixhawk [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
Figure 16
Figure 16. Figure 16: Experiment 13: the UAV navigates among five dynamic obstacles [PITH_FULL_IMAGE:figures/full_fig_p020_16.png] view at source ↗
Figure 15
Figure 15. Figure 15: UAV’s velocity profile in Experiment 10. The UAV satisfies the [PITH_FULL_IMAGE:figures/full_fig_p020_15.png] view at source ↗
read the original abstract

SANDO is a safe trajectory planner for 3D dynamic unknown environments, where obstacle locations and motions are unknown a priori and a collision-free plan can become unsafe at any moment, requiring fast replanning. Existing soft-constraint planners are fast but cannot guarantee collision-free paths, while hard-constraint methods ensure safety at the cost of longer computation. SANDO addresses this trade-off through three contributions. First, a heat map-based A* global planner steers paths away from high-risk regions using soft costs, and a spatiotemporal safe flight corridor (STSFC) generator produces time-layered polytopes that inflate obstacles only by their worst-case reachable set at each time layer, rather than by the worst case over the entire horizon. Second, trajectory optimization is formulated as a Mixed-Integer Quadratic Program (MIQP) with hard collision-avoidance constraints, and a variable elimination technique reduces the number of decision variables, enabling fast computation. Third, a formal safety analysis establishes collision-free guarantees under explicit velocity-bound and estimation-error assumptions. Ablation studies show that variable elimination yields up to 7.4x speedup in optimization time, and that STSFCs are critical for feasibility in dense dynamic environments. Benchmark simulations against state-of-the-art methods across standardized static benchmarks, obstacle-rich static forests, and dynamic environments show that SANDO consistently achieves the highest success rate with no constraint violations across all difficulty levels; perception-only experiments without ground truth obstacle information confirm robust performance under realistic sensing. Hardware experiments on a UAV with fully onboard planning, perception, and localization demonstrate six safe flights in static environments and ten safe flights among dynamic obstacles.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript presents SANDO, a trajectory planner for 3D dynamic unknown environments. It combines a heat-map A* global planner that avoids high-risk regions via soft costs, a spatiotemporal safe flight corridor (STSFC) generator that produces time-layered polytopes by inflating each obstacle only with its per-timestep worst-case reachable set, an MIQP trajectory optimizer with hard collision-avoidance constraints and a variable-elimination technique to reduce decision variables, and a formal safety analysis under explicit velocity-bound and bounded-estimation-error assumptions. Ablation studies report up to 7.4x optimization speedup from variable elimination and improved feasibility from STSFCs; benchmarks across static, forest, and dynamic scenarios claim highest success rates with zero constraint violations; perception-only and hardware UAV trials are also reported.

Significance. If the formal safety analysis is correct and the benchmark comparisons are fair, the work offers a practical advance in trading off speed and guaranteed safety for UAVs in partially unknown dynamic settings. The STSFC construction (tighter than full-horizon inflation) and the variable-elimination speedup are concrete engineering contributions that could be adopted by other hard-constraint planners. The hardware demonstration of fully onboard planning strengthens the practical relevance.

major comments (3)
  1. [Formal safety analysis] Formal safety analysis: the collision-free guarantee is derived under the modeling assumptions that obstacle velocities are known and bounded and that estimation errors are bounded. The manuscript's simulations and hardware trials use obstacles whose motion exactly respects the same velocity bounds employed by the planner; no sensitivity analysis or trials with bound violations (e.g., brief accelerations exceeding the declared speed) are provided. Because the central safety claim for unknown environments rests on these assumptions, the lack of robustness evidence is load-bearing.
  2. [STSFC generator] STSFC generator and MIQP constraints: the reachable-set inflation is performed per time layer rather than over the full horizon, which improves feasibility but makes the hard polytope constraints valid only if the per-layer over-approximation contains every possible obstacle position at that instant. The manuscript does not quantify the tightness of the reachable-set over-approximation or show that the resulting polytopes remain valid under the stated estimation-error bounds; this directly affects the “no constraint violations” benchmark claim.
  3. [Trajectory optimization] Variable elimination in the MIQP: the technique is reported to yield up to 7.4x speedup while preserving feasibility. Without an explicit statement (or proof sketch) that the eliminated variables do not relax the hard collision-avoidance inequalities, it is unclear whether the reduced problem remains equivalent to the original MIQP; this is central to the claim that hard constraints are maintained at reduced cost.
minor comments (2)
  1. [Abstract] The abstract states “six safe flights in static environments and ten safe flights among dynamic obstacles” but provides no quantitative metrics (e.g., minimum clearance, replanning frequency, or failure modes) for these trials.
  2. [Benchmark results] Figure captions and table headings should explicitly state whether the reported success rates and computation times are averaged over how many Monte-Carlo runs and whether error bars or standard deviations are shown.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough and constructive review. The comments help clarify the scope of our safety claims and strengthen the presentation of the technical contributions. We respond point-by-point to the major comments below.

read point-by-point responses

  1. Referee: Formal safety analysis: the collision-free guarantee is derived under the modeling assumptions that obstacle velocities are known and bounded and that estimation errors are bounded. The manuscript's simulations and hardware trials use obstacles whose motion exactly respects the same velocity bounds employed by the planner; no sensitivity analysis or trials with bound violations (e.g., brief accelerations exceeding the declared speed) are provided. Because the central safety claim for unknown environments rests on these assumptions, the lack of robustness evidence is load-bearing.

    Authors: We agree that the collision-free guarantee in Section IV is conditional on the explicit assumptions of bounded obstacle velocities and bounded estimation errors. All reported simulations and hardware trials operate strictly inside these bounds, consistent with the standard 'unknown but bounded' modeling framework used in robust motion planning. We acknowledge that sensitivity analysis under deliberate bound violations is absent and would provide additional insight into practical robustness. In the revised manuscript we will expand the Limitations section to discuss the consequences of bound violations and to recommend the use of conservative velocity and error bounds in deployment. New empirical trials that intentionally violate the bounds lie outside the scope of the present work but are noted as valuable future validation. revision: partial

  2. Referee: STSFC generator and MIQP constraints: the reachable-set inflation is performed per time layer rather than over the full horizon, which improves feasibility but makes the hard polytope constraints valid only if the per-layer over-approximation contains every possible obstacle position at that instant. The manuscript does not quantify the tightness of the reachable-set over-approximation or show that the resulting polytopes remain valid under the stated estimation-error bounds; this directly affects the “no constraint violations” benchmark claim.

    Authors: The STSFC construction inflates each obstacle at every discrete time layer by its worst-case reachable set under the velocity bound and then further enlarges the polytope by the estimation-error radius ε. Under the paper's assumptions this guarantees containment of every possible obstacle position at that instant. To address the request for explicit quantification, the revised manuscript will add a short lemma in Section III-B that (i) states the containment property formally and (ii) provides a simple volume-based bound on the over-approximation tightness for the chosen reachable-set model. This addition will directly support the validity of the hard polytope constraints and the reported zero-violation results. revision: yes

  3. Referee: Variable elimination in the MIQP: the technique is reported to yield up to 7.4x speedup while preserving feasibility. Without an explicit statement (or proof sketch) that the eliminated variables do not relax the hard collision-avoidance inequalities, it is unclear whether the reduced problem remains equivalent to the original MIQP; this is central to the claim that hard constraints are maintained at reduced cost.

    Authors: The variable-elimination procedure substitutes only those decision variables that are affine functions of the retained variables (primarily positions expressed via integrated velocity/acceleration). Because the collision-avoidance inequalities are linear in the position variables, the substitution preserves the feasible set exactly; no relaxation is introduced. The revised manuscript will include a concise proof sketch in the appendix demonstrating equivalence of the reduced and original MIQPs with respect to both feasibility and the optimal objective value. This will confirm that the reported speed-up is achieved without weakening the hard constraints. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation rests on external assumptions and standard optimization techniques

full rationale

The paper presents algorithmic contributions (heat-map A*, STSFC generation, MIQP variable elimination) and a formal safety analysis conditioned on explicit inputs (velocity bounds, bounded estimation error). These do not reduce by construction to fitted parameters, self-citations, or renamed known results. The collision-free guarantees are stated as holding only under the listed modeling assumptions rather than being derived tautologically from the planner's own outputs. No load-bearing step equates a prediction to its own input via definition or self-reference.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim depends on domain assumptions about bounded obstacle velocities and estimation errors plus the new STSFC construction; no free parameters are explicitly fitted in the abstract, and no new physical entities are postulated beyond algorithmic constructs.

axioms (2)
  • domain assumption Obstacles have unknown motions but bounded velocities
    Invoked to compute worst-case reachable sets for per-time-layer corridor inflation
  • domain assumption Estimation and sensing errors are bounded
    Required for the formal collision-free guarantee
invented entities (1)
  • Spatiotemporal Safe Flight Corridor (STSFC) no independent evidence
    purpose: Time-layered polytopes that inflate obstacles only by their worst-case reachable set at each time layer
    Core new construct enabling less conservative hard constraints than global worst-case inflation

pith-pipeline@v0.9.0 · 5594 in / 1524 out tokens · 59936 ms · 2026-05-10T16:57:09.178741+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

39 extracted references · 39 canonical work pages

  1. [1]

    Ego-planner: An esdf- free gradient-based local planner for quadrotors,

    X. Zhou, Z. Wang, H. Ye, C. Xu, and F. Gao, “Ego-planner: An esdf- free gradient-based local planner for quadrotors,”IEEE Robotics and Automation Letters, vol. 6, no. 2, pp. 478–485, 2021

    work page 2021

  2. [2]

    Faster: Fast and safe trajectory planner for navigation in unknown environments,

    J. Tordesillas, B. T. Lopez, M. Everett, and J. P. How, “Faster: Fast and safe trajectory planner for navigation in unknown environments,” IEEE Transactions on Robotics, vol. 38, no. 2, pp. 922–938, 2022

    work page 2022

  3. [3]

    High-speed motion planning for aerial swarms in unknown and cluttered environments,

    C. Toumieh and D. Floreano, “High-speed motion planning for aerial swarms in unknown and cluttered environments,”IEEE Transactions on Robotics, vol. 40, pp. 3642–3656, 2024

    work page 2024

  4. [4]

    Safety-assured high-speed navigation for mavs,

    Y. Ren, F. Zhu, G. Lu, Y. Cai, L. Yin, F. Kong, J. Lin, N. Chen, and F. Zhang, “Safety-assured high-speed navigation for mavs,”Science Robotics, vol. 10, no. 98, p. eado6187, 2025

    work page 2025

  5. [5]

    Uavdynamic path planning based on obstacle position prediction in an unknown environment,

    J.Feng,J.Zhang,G.Zhang,S.Xie,Y.Ding,andZ.Liu,“Uavdynamic path planning based on obstacle position prediction in an unknown environment,”IEEE Access, vol. 9, pp. 154679–154691, 2021

    work page 2021

  6. [6]

    Vision-aided uav navigation and dynamic obstacle avoidance using gradient-based b-spline trajectory optimization,

    Z. Xu, Y. Xiu, X. Zhan, B. Chen, and K. Shimada, “Vision-aided uav navigation and dynamic obstacle avoidance using gradient-based b-spline trajectory optimization,”arXiv preprint arXiv:2209.07003, 2022

    work page arXiv 2022

  7. [7]

    Fapp:Fastandadaptiveperception and planning for uavs in dynamic cluttered environments,

    M.Lu,X.Fan,H.Chen,andP.Lu,“Fapp:Fastandadaptiveperception and planning for uavs in dynamic cluttered environments,”IEEE Transactions on Robotics, vol. 41, pp. 871–886, 2025

    work page 2025

  8. [8]

    Risk-aware enabled path planning for drones flight in unknown environment,

    Z. Zong, D. Li, X. Dong, Y. Cui, B. Yang, J. Xiang, and Z. Tu, “Risk-aware enabled path planning for drones flight in unknown environment,”JournalofIntelligent&RoboticSystems,vol.111,2025

    work page 2025

  9. [9]

    Flying in highly dynamic environments with end-to-end learning approach,

    X. Fan, M. Lu, B. Xu, and P. Lu, “Flying in highly dynamic environments with end-to-end learning approach,”IEEE Robotics and Automation Letters, vol. 10, no. 4, pp. 3851–3858, 2025

    work page 2025

  10. [10]

    Robust vision-based obstacle avoidance for micro aerial vehicles in dynamic environments,

    J. Lin, H. Zhu, and J. Alonso-Mora, “Robust vision-based obstacle avoidance for micro aerial vehicles in dynamic environments,” in2020 IEEE International Conference on Robotics and Automation (ICRA), pp. 2682–2688, IEEE, 2020

    work page 2020

  11. [12]

    Tight collision probability for uav motion planning in uncertain environment,

    T. Liu, F. Zhang, F. Gao, and J. Pan, “Tight collision probability for uav motion planning in uncertain environment,” in2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 1055–1062, 2023

    work page 2023

  12. [13]

    Recursively feasible shrinking-horizon mpc in dynamic environments with conformal pre- diction guarantees,

    C. Stamouli, L. Lindemann, and G. Pappas, “Recursively feasible shrinking-horizon mpc in dynamic environments with conformal pre- diction guarantees,” in6th Annual Learning for Dynamics & Control Conference, pp. 1330–1342, PMLR, 2024

    work page 2024

  13. [14]

    A state-time space approach for local trajectory replanning of an mav in dynamic indoor environments,

    F. Quan, Y. Shen, P. Liu, X. Lyu, and H. Chen, “A state-time space approach for local trajectory replanning of an mav in dynamic indoor environments,”IEEE Robotics and Automation Letters, vol. 10, no. 4, pp. 3438–3445, 2025

    work page 2025

  14. [15]

    Intent prediction- driven model predictive control for uav planning and navigation in dynamic environments,

    Z. Xu, H. Jin, X. Han, H. Shen, and K. Shimada, “Intent prediction- driven model predictive control for uav planning and navigation in dynamic environments,”IEEE Robotics and Automation Letters, vol. 10, no. 5, pp. 4946–4953, 2025

    work page 2025

  15. [16]

    Panther: Perception-aware trajectory planner in dynamic environments,

    J. Tordesillas and J. P. How, “Panther: Perception-aware trajectory planner in dynamic environments,”IEEE Access, vol. 10, pp. 22662– 22677, 2022

    work page 2022

  16. [17]

    Swarm of micro flying robots in the wild,

    X. Zhou, X. Wen, Z. Wang, Y. Gao, H. Li, Q. Wang, T. Yang, H. Lu, Y. Cao, C. Xu, and F. Gao, “Swarm of micro flying robots in the wild,”Science Robotics, vol. 7, no. 66, p. eabm5954, 2022

    work page 2022

  17. [18]

    Heuristic-based incre- mental probabilistic roadmap for efficient uav exploration in dynamic environments,

    Z. Xu, C. Suzuki, X. Zhan, and K. Shimada, “Heuristic-based incre- mental probabilistic roadmap for efficient uav exploration in dynamic environments,” in2024 IEEE International Conference on Robotics and Automation (ICRA), pp. 11832–11838, 2024

    work page 2024

  18. [19]

    Efficient mixed-integer planning for uavs in cluttered environments,

    R. Deits and R. Tedrake, “Efficient mixed-integer planning for uavs in cluttered environments,” in2015 IEEE International Conference on Robotics and Automation (ICRA), pp. 42–49, 2015

    work page 2015

  19. [20]

    Aggressive quadrotor flight through cluttered environments using mixed integer programming,

    B. Landry, R. Deits, P. R. Florence, and R. Tedrake, “Aggressive quadrotor flight through cluttered environments using mixed integer programming,” in2016 IEEE international conference on robotics and automation (ICRA), pp. 1469–1475, IEEE, 2016

    work page 2016

  20. [21]

    Geometrically constrained tra- jectory optimization for multicopters,

    Z. Wang, X. Zhou, C. Xu, and F. Gao, “Geometrically constrained tra- jectory optimization for multicopters,”IEEE Transactions on Robotics, vol. 38, no. 5, pp. 3259–3278, 2022

    work page 2022

  21. [22]

    Motion planning in dynamic environments using velocity obstacles,

    P. Fiorini and Z. Shiller, “Motion planning in dynamic environments using velocity obstacles,”The international journal of robotics re- search, vol. 17, no. 7, pp. 760–772, 1998

    work page 1998

  22. [23]

    Control barrier functions: Theory and applications,

    A. D. Ames, S. Coogan, M. Egerstedt, G. Notomista, K. Sreenath, and P. Tabuada, “Control barrier functions: Theory and applications,” in 2019 18th European control conference (ECC), pp. 3420–3431, Ieee, 2019

    work page 2019

  23. [24]

    Hamilton–jacobi reachability: Some recent theoretical advances and applications in unmanned airspace 21 management,

    M. Chen and C. J. Tomlin, “Hamilton–jacobi reachability: Some recent theoretical advances and applications in unmanned airspace 21 management,”Annual Review of Control, Robotics, and Autonomous Systems, vol. 1, no. 1, pp. 333–358, 2018

    work page 2018

  24. [25]

    Planning dynamically feasible trajectories for quadrotors using safe flight corridors in 3-d complex environments,

    S. Liu, M. Watterson, K. Mohta, K. Sun, S. Bhattacharya, C. J. Taylor, and V. Kumar, “Planning dynamically feasible trajectories for quadrotors using safe flight corridors in 3-d complex environments,” IEEE Robotics and Automation Letters, vol. 2, no. 3, pp. 1688–1695, 2017

    work page 2017

  25. [26]

    Computing large convex regions of obstacle- free space through semidefinite programming,

    R. Deits and R. Tedrake, “Computing large convex regions of obstacle- free space through semidefinite programming,” inAlgorithmic Foun- dations of Robotics XI: Selected Contributions of the Eleventh Interna- tional Workshop on the Algorithmic Foundations of Robotics, pp. 109– 124, Springer, 2015

    work page 2015

  26. [27]

    Mixed-integer quadratic program trajectory generation for heterogeneous quadrotor teams,

    D. Mellinger, A. Kushleyev, and V. Kumar, “Mixed-integer quadratic program trajectory generation for heterogeneous quadrotor teams,” in2012 IEEE international conference on robotics and automation, pp. 477–483, IEEE, 2012

    work page 2012

  27. [28]

    Nocedal and S

    J. Nocedal and S. J. Wright,Numerical optimization. Springer, 2006

    work page 2006

  28. [29]

    Polynomial trajectory planning for aggressive quadrotor flight in dense indoor environments,

    C. Richter, A. Bry, and N. Roy, “Polynomial trajectory planning for aggressive quadrotor flight in dense indoor environments,” inRobotics Research: The 16th International Symposium ISRR, pp. 649–666, Springer, 2016

    work page 2016

  29. [30]

    Raptor: Robust and perception- aware trajectory replanning for quadrotor fast flight,

    B. Zhou, J. Pan, F. Gao, and S. Shen, “Raptor: Robust and perception- aware trajectory replanning for quadrotor fast flight,”IEEE Transac- tions on Robotics, vol. 37, no. 6, pp. 1992–2009, 2021

    work page 1992

  30. [31]

    G. E. Farin,Curves and surfaces for CAGD: a practical guide. Morgan Kaufmann, 2002

    work page 2002

  31. [32]

    Gurobi Optimizer Reference Manual,

    Gurobi Optimization, LLC, “Gurobi Optimizer Reference Manual,” 2024

    work page 2024

  32. [33]

    Dynablox: Real-time detection of diverse dynamic objects in complex environments,

    L. Schmid, O. Andersson, A. Sulser, P. Pfreundschuh, and R. Siegwart, “Dynablox: Real-time detection of diverse dynamic objects in complex environments,”IEEE Robotics and Automation Letters, vol. 8, no. 10, pp. 6259–6266, 2023

    work page 2023

  33. [34]

    Adaptive adjustment of noise covariance in kalman filter for dynamic state estimation,

    S. Akhlaghi, N. Zhou, and Z. Huang, “Adaptive adjustment of noise covariance in kalman filter for dynamic state estimation,” in2017 IEEE Power & Energy Society General Meeting, pp. 1–5, 2017

    work page 2017

  34. [35]

    Oa-mpc: Occlusion-aware mpc for guaranteed safe robot navigation with unseen dynamic obstacles,

    R. Firoozi, A. Mir, G. S. Camps, and M. Schwager, “Oa-mpc: Occlusion-aware mpc for guaranteed safe robot navigation with unseen dynamic obstacles,”IEEE Transactions on Control Systems Technol- ogy, vol. 33, no. 3, pp. 940–951, 2025

    work page 2025

  35. [36]

    Guaranteed infinite horizon avoidance of unpredictable,dynamicallyconstrainedobstacles,

    A. Wu and J. P. How, “Guaranteed infinite horizon avoidance of unpredictable,dynamicallyconstrainedobstacles,”Autonomousrobots, vol. 32, no. 3, pp. 227–242, 2012

    work page 2012

  36. [37]

    On the limited memory bfgs method for large scale optimization,

    D. C. Liu and J. Nocedal, “On the limited memory bfgs method for large scale optimization,”Mathematical programming, vol. 45, no. 1, pp. 503–528, 1989

    work page 1989

  37. [38]

    Directlidar-inertialodometry: Lightweight lio with continuous-time motion correction,

    K.Chen,R.Nemiroff,andB.T.Lopez,“Directlidar-inertialodometry: Lightweight lio with continuous-time motion correction,” in2023 IEEE International Conference on Robotics and Automation (ICRA), pp. 3983–3989, 2023

    work page 2023

  38. [39]

    Px4: A node-based multithreaded open source robotics framework for deeply embedded platforms,

    L. Meier, D. Honegger, and M. Pollefeys, “Px4: A node-based multithreaded open source robotics framework for deeply embedded platforms,” in2015 IEEE International Conference on Robotics and Automation (ICRA), pp. 6235–6240, 2015

    work page 2015

  39. [40]

    Pixhawk: A system for autonomous flight using onboard computer vision,

    L. Meier, P. Tanskanen, F. Fraundorfer, and M. Pollefeys, “Pixhawk: A system for autonomous flight using onboard computer vision,” in 2011 IEEE International Conference on Robotics and Automation, pp. 2992–2997, 2011. 22

    work page 2011