A Hybrid Method for Online Trajectory Planning of Mobile Robots in Cluttered Environments

David G\'omez-Guti\'errez; Jos\'e I. Parra-Vilchis; Leobardo Campos-Mac\'ias; Rafael de la Guardia; Rodrigo Aldana-L\'opez

REVIEW 4 major objections 3 minor 27 references

A Hybrid Method for Online Trajectory Planning of Mobile Robots in Cluttered Environments

T0 review · 4 major / 3 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper shows that a sampling-based path can be turned into a dynamically feasible, collision-free trajectory by a single convex quadratic program, with a worst-case deviation bound that makes iterative optimization unnecessary.

desk verdict The paper's core promise of a guaranteed-feasible single-shot QP is undercut by an algebraic error in the kinematics that breaks the central theorem, though the idea and experiments are worth a serious revision. read the letter →

arxiv 1908.08493 v1 pith:PP7UU2OV submitted 2019-08-22 cs.RO

Leobardo Campos-Macías , David Gómez-Gutiérrez , Rodrigo Aldana-López , Rafael de la Guardia , José I. Parra-Vilchis This is my paper · ORCID

classification cs.RO

keywords trajectoryplanningsampling-basedpathquadraticprogrammingconvexoptimizationcollisionavoidanceonlinequadcopternavigationclutteredenvironments

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that online trajectory planning in a known cluttered environment can be split into two stages: a sampling-based planner finds an obstacle-free piecewise-linear path, and a single convex quadratic program turns that path into a time-parameterized trajectory respecting velocity and acceleration limits. The central guarantee is that the QP is always feasible, so no iterative or sequential convex programming is needed, and that the resulting continuous trajectory stays within $\frac{3}{2}\ell\sqrt{d}$ of the guiding path, making it collision-free at every instant and not just at sampled waypoints. If this claim holds, dense-environment navigation can combine the reliability of sampling-based planners with the speed of convex optimization, which is why the authors report very high success rates and planning times of a fraction of a second on quadcopter experiments.

What carries the argument

The load-bearing construction is the sequence of time-indexed waypoints $\varpi[k]$ with hypercube soft constraints $\Omega[k]$. Each waypoint sits on the sampled path, consecutive waypoints are separated by $\ell$, and two identical waypoints are placed at every path vertex. The dynamical constants $V_{\max}=\sqrt{\ell A_{\max}}$ and $h=2\sqrt{\ell/A_{\max}}$ are chosen so that crossing one hypercube in one time step is always possible with bounded acceleration; the duplicated vertex waypoints provide the extra time step needed to reverse direction safely. These choices make the QP's constraint set nonempty by construction, and the separation argument in Lemma 7 turns that into a continuous-time collision-free guarantee.

What would settle it

Run the planner in an environment where the true minimum clearance of the sampled path is measured, set $\ell$ so that $\ell_m < \frac{3}{2}\ell\sqrt{d}$, solve the QP, and check whether the executed continuous trajectory enters the inflated obstacle region. If it does in any such case, the unconditional collision-free claim is false; if it never does for $\ell=0.05$ with nominal clearance $0.05$ m in 3D, the bound is conservative or the realized clearance exceeds the nominal one.

Watch

Extended reading notes

Core claim

The paper's core discovery is a constructive choice of waypoint spacing and time step that makes the feasibility problem trivial to satisfy. Along the sampled path it places waypoints $\varpi[k]$ at Euclidean spacing $\ell$, with duplicate waypoints at every vertex to handle sharp turns, and associates each with a hypercube $\Omega[k]=\{\rho : \|\rho-\varpi[k]\|_\infty\le \ell\}$. Choosing $V_{\max}^2=\ell A_{\max}$ and $h^2=4\ell/A_{\max}$, the authors prove through Lemmas 5-7 that a piecewise-constant acceleration exists moving the robot from any state in one hypercube to the next while respecting velocity and acceleration bounds, and that between samples the trajectory cannot depart more than $\frac{3}{2}\ell\sqrt{d}$ from the guiding path. The QP then only has to minimize a cost such as jerk subject to these hypercube and bound constraints, and by Theorem 3 it is guaranteed feasible. This converts trajectory planning from a search over time durations and waypoint counts into a one-shot convex solve.

Load-bearing premise

The collision-free guarantee assumes the sampled path truly keeps a minimum distance from obstacles of at least $\frac{3}{2}\ell\sqrt{d}$, an inequality the paper never writes out; its benchmarks use $\ell=0.05$ in 3D, which allows about $0.13$ m of deviation against a nominal clearance of $0.05$ m.

Editorial extensions

If this is right

A trajectory for a robot with bounded acceleration can be computed by solving one convex QP, so planning can run at the few-hundred-millisecond scale even in environments with hundreds of obstacles.
Because the QP is guaranteed feasible whenever the sampling planner finds a path with the required clearance, the overall success rate is essentially inherited from the sampling planner and is not degraded by the optimization stage.
The continuous trajectory, not just the discrete samples, is collision-free, so no post-hoc interpolation check or iterative time adjustment is needed.
The design parameter $\ell$ controls a clear trade-off: smaller $\ell$ gives shorter trajectories but longer solve times, while larger $\ell$ produces faster solves and larger clearance margins.
Replanning can be triggered online while the robot executes a committed segment, supporting goal changes in obstacle-dense environments without restarting the whole pipeline.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

An implied tuning rule, not written in the paper, is to cap the deviation budget at about $0.38$ times the path's minimum clearance in three dimensions; this follows directly from the stated separation bound and gives a concrete safety-margin recipe for users.
Because the QP constraints only involve velocity and acceleration bounds, the same waypoint-hypercube construction should transfer to other differentially flat vehicles, not just quadcopters, by substituting the vehicle's acceleration limit.
The paper's table showing solve time decreasing as $\ell$ grows suggests an online planner could adapt $\ell$ during replanning, starting with a large margin for a fast initial solve and shrinking it later to shorten the trajectory.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Here's the short version: the paper has a nice, potentially useful idea—construct time-indexed waypoints along a sampling-based path and derive explicit Vmax and h so that a single convex QP is guaranteed feasible, avoiding iterative SCP. The experimental work is real: a Crazyflie flying through dense 3D obstacle fields, with comparisons to iSCP and CHOMP that show a clear edge in success rate and time. If the theory matched the implementation, this would be a solid RA-L contribution.

Unfortunately, it doesn't match. The kinematics in Problem 4 are algebraically wrong. Under the stated constant-acceleration dynamics, the correct expansion is p[k] = p[0] + h k v[0] + h^2 Σ_{i=0}^{k-1} (k - i - 1/2) a[i]. The paper instead uses (h^2/2) Σ (2(k-i)+3) a[i], which is off by a factor of 5 for k=1 and inconsistent for every term. That's not a typo; the QP constraints are written with this erroneous p[k], so a feasible solution of the QP as posed does not satisfy the claimed waypoint constraints under the actual dynamics. Theorem 3, which is supposed to bound the trajectory deviation, therefore does not apply to the trajectory the robot would execute. This is load-bearing.

Two smaller gaps are worth noting. Lemma 5 assumes consecutive waypoints are exactly 𝓁 apart, but the construction uses ceil(‖η[s+1]−η[s]‖/𝓁), giving spacing ≤ 𝓁 plus duplicate waypoints at path nodes; this needs rework. And the collision-free guarantee silently requires a clearance inequality, 𝓁_m ≥ (3/2)𝓁√d, that is never stated; the benchmark uses 𝓁=0.05 in 3D, which would need about 0.13m clearance while they mention 0.05m. The authors may have inflated obstacles separately, but the paper should say so explicitly.

The empirical results are suggestive but don't rescue the theory: the QP solver is finding trajectories that work in practice, but the paper's central claim—guaranteed feasibility and collision-freedom—is not established. I don't see evidence of bad faith; the references are relevant and the approach is clearly a serious attempt. I just think the main theorem is broken as written.

Who should read it: robotics people interested in hybrid sampling+optimization planning, and anyone who wants to see how a small algebraic slip can undermine a guarantee. I would not cite it as a correctness result until fixed.

If this were submitted fresh, I'd send it out—the idea deserves a serious referee and the errors look repairable. But I would expect major revision: fix the kinematics, redo Lemma 5 with the actual waypoint spacing, and state the clearance inequality. As it stands, it's not acceptable.

Referee Report

4 major / 3 minor

Summary. The paper proposes a hybrid online trajectory planning method: an IRRT* sampling-based planner generates an obstacle-free path, and a single convex QP computes a time-parameterized trajectory that is claimed to be guaranteed feasible and collision-free. The QP uses waypoints placed along the path with associated hypercube regions, and the time step and velocity bound are derived from a design parameter 𝓁 and the maximum acceleration. The central theoretical claims are that the QP is always feasible and that the continuous trajectory remains within (3/2)𝓁√d of the path, hence collision-free given sufficient path clearance. The method is compared with iSCP and CHOMP in simulation and demonstrated on a Crazyflie quadcopter in cluttered environments with up to 200 obstacles.

Significance. If the theoretical claims were correct, the paper would make a valuable contribution: replacing iterative or sequential convex programs with a single QP that has formal feasibility and collision-avoidance guarantees is an important step for online planning. The experimental work is substantial, including 500-trial benchmarks across varying obstacle densities and real quadcopter flights, and the algorithm is clearly described with parameter choices. However, the correctness of the central guarantees is not established by the manuscript. The algebraic error in the discrete kinematics of Problem 4 and the invalid coordinate-wise arguments in the Appendix undermine the proof of the main theorem. The empirical results, while promising, cannot compensate for these theoretical gaps.

major comments (4)

[Section IV, Problem 4] The discrete-time kinematics used in Problem 4 are algebraically incorrect. Under the stated constant-acceleration model, where a[i] is held constant on (ih,(i+1)h], the exact recurrence p[k+1]=p[k]+h v[k]+(h^2/2)a[k], v[k+1]=v[k]+h a[k] yields p[k] = p[0] + h k v[0] + h^2 Σ_{i=0}^{k-1} (k-i-1/2) a[i]. The paper instead defines the coefficient as (2(k-i)+3)/2 = k-i+3/2, which is larger by 2 for every term. Consequently, the constraints ‖ϖ[k]-p[k]‖∞ ≤ 𝓁 in Problem 4 are evaluated at positions that do not equal the actual positions produced by the acceleration sequence under the stated dynamics. A QP solution can therefore satisfy all constraints as written while the executed trajectory violates the waypoint constraints and the separation bound of Theorem 3. This error is load-bearing because the paper's central claim is that the posed QP is guaranteed feasible and that its solution is collision-free; the appendix lemmas construct accelerations using the correct recurrence, so the QP as stated is not the problem those lemmas solve.
[Appendix, Lemma 5] The proof of Lemma 5, and similarly Lemma 6, uses a rotation of coordinates so that the path segment lies on the x-axis, and then performs the construction coordinate-wise under assumptions such as vx[k] ∈ [0,Vmax], vy[k] ∈ [-Vmax,Vmax], and Ω[k+1] = Ω[k] + [𝓁,0,...]^T. These assertions are not valid for the ∞-norm constraints used in the paper. The ∞-norm is not invariant under rotation: for v with ‖v‖∞ ≤ Vmax, a rotated component can be as large as √d Vmax. Moreover, the rotation of an axis-aligned hypercube Ω[k] is generally not an axis-aligned hypercube in the rotated frame, so the coordinate-wise bounds on p[k] and the shifted-cube relation do not hold. Thus the constructed acceleration may violate the original acceleration bound and may not drive p[k+1] into Ω[k+1]. This invalidates the derivation of the feasibility conditions in Problem 2 and the proof of Theorem 3.
[Section IV-A and Lemma 5] The feasibility proof assumes that consecutive waypoints are exactly 𝓁 apart (Problem 2, condition (i)), but the construction in Section IV-A sets κ_s = ceil(‖η[s+1]-η[s]‖/𝓁), giving spacing δ ≤ 𝓁, and adds duplicate waypoints at path nodes. The control designed in Lemma 5 produces a displacement of exactly 𝓁 along the path direction; when δ < 𝓁, a robot starting at the maximal allowable position in Ω[k] can be sent beyond Ω[k+1], so the proof does not cover the actual waypoint sequence generated by the algorithm. The paper does not explain how Problem 2's conditions are satisfied by the construction with non-uniform spacing and duplicate waypoints; Lemma 6 addresses duplicate waypoints but inherits the same rotation issues.
[Section IV, Theorem 3] The claim that the bound |b(t)| ≤ (3/2)𝓁√d implies p(t) ∈ χFree requires a quantitative relationship between the path clearance 𝓁_m and the design parameter 𝓁. The paper asserts that 'Since there is a minimum clearance of 𝓁_m, this property guarantees a collision-free trajectory,' but it never states the required inequality 𝓁_m ≥ (3/2)𝓁√d. In the simulation benchmarks, 𝓁 = 0.05 is used in three dimensions, giving a deviation bound of approximately 0.13 m, while the reported clearance values are not shown to satisfy this inequality. In the experiments, 𝓁 = 0.02 yields a deviation bound of approximately 0.052 m, yet the stated maximum allowable 𝓁 derived from the robot radius, string diameter, and tracking error is 0.035 m, which would not satisfy the inequality if 𝓁_m = 0.035 m. Without this condition, Theorem 3 does not establish collision avoidance.

minor comments (3)

[Section IV, Problem 2 and Problem 4] There are several minor typographical issues: 'assumme' appears in Problem 2; the subscripts in the waypoint definition are inconsistently typeset (ϖs versus ϖ_s); and the dimension of the optimization variable in Problem 4 is written as R^{dK} although there are K+1 acceleration vectors, so the dimension should be d(K+1).
[Figure 4 caption] The caption of Figure 4 states that the separation is 'bounded by 2/3 𝓁√d', while the text and Theorem 3 give the bound as (3/2)𝓁√d. The fraction appears inverted in the caption.
[Section II and Lemma 7] The definition of b(t) as a minimum of distances is nonnegative by construction, so the notation |b(t)| used in Lemma 7 and Theorem 3 is inconsistent; if b(t) is intended to be signed, its definition and the bound should be clarified.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: central guarantees are analytic constructions, not fits or self-citations.

full rationale

No circular step is present. The feasibility guarantee (Theorem 3) is supported by Lemmas 5–7, which supply explicit constant-acceleration constructions from the stated inputs (𝕉, Amax, path waypoints); the proof does not assume the QP solution exists and does not fit any parameter to a target outcome. The collision-free bound |b(t)|≤(3/2)𝕉√d is derived analytically from the waypoint-box constraints, not renamed from them, and the extra requirement that this bound fit within the obstacle clearance 𝕉_m is a design condition even though the inequality 𝕉_m ≥ (3/2)𝕉√d is not written out explicitly. The QP in Problem 4 uses the same waypoint regions as constraints, but feasibility is established by an independent existence argument, so the formulation does not reduce to its inputs by construction. The performance and success-rate claims are empirical comparisons against iSCP and CHOMP, not outputs derived from fitted parameters. The paper contains no load-bearing self-citations: IRRT*, RRT*, CHOMP, iSCP, and the differential-flatness result are external standard references. The apparent algebraic discrepancy between the closed-form p[k] in Problem 4 and the constant-acceleration recurrence used in the lemmas, if real, is a correctness bug rather than a circularity; likewise, the unstated clearance inequality is an assumption or robustness gap, not a circular reduction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central guarantee rests on a double-integrator particle model, known static obstacles, a piecewise-linear path with clearance, an exact-spacing assumption that the construction does not satisfy, and implicit alignment of velocity with path direction. The design parameters 𝓁 and Amax are hand-chosen inputs. No new physical entities are introduced.

free parameters (3)

𝓁 (design clearance parameter) = 0.05 m in benchmark, 0.02 m in experiments
Controls waypoint spacing, hypercube size, and the allowed trajectory deviation from the path. Chosen by hand, balancing QP size against trajectory length.
Amax (maximum acceleration) = 20 m/s^2
Maximum acceleration per axis, chosen by trial and error in the experiments. Together with 𝓁 it determines Vmax and h.
IRRT* planning budget = At most 4 rounds, early stop if no cost improvement
Anytime planning limit selected by the authors; affects path quality and computation time but not the core feasibility theorem.

assumptions (5)

domain assumption The robot centroid obeys double-integrator dynamics pdot = v, vdot = a with per-axis acceleration bounds.
Used throughout Section II and IV. Justified for quadcopters by differential flatness with citation [19], but it is a modeling assumption.
domain assumption The obstacle region is known and static, and obstacles can be inflated before path planning.
Problem 1 assumes knowledge of the environment; the method relies on obstacle inflation to create clearance.
domain assumption The sampling-based planner returns a piecewise-linear obstacle-free path with a known positive minimum clearance 𝓁_m.
The feasibility and collision-free guarantees are stated relative to such a path. The paper does not specify how 𝓁_m is measured in practice.
ad hoc to paper Consecutive waypoints in the feasibility proof are exactly 𝓁 apart.
Problem 2 condition i and Lemma 5 assume ‖ϖ[k+1]−ϖ[k]‖₂ = 𝓁, but the construction with κ_s = ceil(‖η[s+1]−η[s]‖/𝓁) yields spacing ≤ 𝓁, plus zero-spacing duplicate waypoints at nodes. The proof does not cover these actual cases.
ad hoc to paper Initial and intermediate velocities are aligned with the path direction, v[k]ᵀ(ϖ[k+1]−ϖ[k]) ≥ 0.
Lemma 5 requires this directional condition. It holds for zero initial velocity, as in the experiments, but is not guaranteed for arbitrary initial states in Problem 1.

how reviews work

0 comments

Cite this review

Pith. "Pith review of A Hybrid Method for Online Trajectory Planning of Mobile Robots in Cluttered Environments." pith.science (2026). https://pith.science/paper/PP7UU2OV

@misc{pith2026190808493,
  author       = {Pith},
  title        = {Pith review of: A Hybrid Method for Online Trajectory Planning of Mobile Robots in Cluttered Environments},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PP7UU2OV}},
  note         = {Machine review of arXiv:1908.08493}
}

read the original abstract

This paper presents a method for online trajectory planning in known environments. The proposed algorithm is a fusion of sampling-based techniques and model-based optimization via quadratic programming. The former is used to efficiently generate an obstacle-free path while the latter takes into account the robot dynamical constraints to generate a time-dependent trajectory. The main contribution of this work lies on the formulation of a convex optimization problem over the generated obstacle-free path that is guaranteed to be feasible. Thus, in contrast with previously proposed methods, iterative formulations are not required. The proposed method has been compared with state-of-the-art approaches showing a significant improvement in success rate and computation time. To illustrate the effectiveness of this approach for online planning, the proposed method was applied to the fluid autonomous navigation of a quadcopter in multiple environments consisting of up to two hundred obstacles. The scenarios hereinafter presented are some of the most densely cluttered experiments for online planning and navigation reported to date. See video at https://youtu.be/DJ1IZRL5t1Q

Figures

Figures reproduced from arXiv: 1908.08493 by the authors.

**Figure 2.** Sketch of the proposed hybrid method for trajectory generation. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Illustration of the proposed hybrid method for trajectory planning. [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: If Vmax and h are a solution to Problem 2, then the robot takes time h to navigate from one point in the discrete trajectory to the next (i.e. p(kh) = p[k], k = 0,...,K) while the separation b(t) between the resulting trajectory p(t) and the continuous path η(s) is bou…

**Figure 5.** Figure 5: Algorithm comparison among iSCP, CHOMP and the proposed approach on different forest environments varying on tree density. Some parameters had to be selected for each algorithm. The iSCP was configured using a total time of 15 seconds and a discretization step of 0.2 s…

**Figure 6.** Figure 6: A composite image of a quadcopter performing a trajectory in a 3x5 [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages

[1]

Real-time motion planning methods for autonomous on-road driving: State-of-the-art and future research directions,

C. Katrakazas, M. Quddus, W.-H. Chen, and L. Deka, “Real-time motion planning methods for autonomous on-road driving: State-of-the-art and future research directions,” Transportation Research Part C: Emerging Technologies, vol. 60, pp. 416 – 442, November 2015

work page 2015
[2]

A survey of motion planning and control techniques for self-driving urban vehicles,

B. Paden, M. Cap, S. Z. Yong, D. Yershov, and E. Frazzoli, “A survey of motion planning and control techniques for self-driving urban vehicles,” IEEE Trans. Intell. Veh., vol. 1, no. 1, pp. 33–55, March 2016

work page 2016
[3]

Sampling-based algorithms for optimal motion planning,

S. Karaman and E. Frazzoli, “Sampling-based algorithms for optimal motion planning,” Int. J. Robot. Res. , vol. 30, no. 7, pp. 846–894, June 2011

work page 2011
[4]

Sampling-based robot motion planning: A review,

M. Elbanhawi and M. Simic, “Sampling-based robot motion planning: A review,” IEEE Access, vol. 2, pp. 56–77, February 2014

work page 2014
[5]

Batch informed trees (BIT*): Sampling-based optimal planning via the heuristically guided search of implicit random geometric graphs,

J. D. Gammell, S. S. Srinivasa, and T. D. Barfoot, “Batch informed trees (BIT*): Sampling-based optimal planning via the heuristically guided search of implicit random geometric graphs,” in IEEE Int. Conf. Robot. Autom., June 2015, pp. 3067–3074

work page 2015
[6]

Regionally accelerated batch informed trees (RABIT*): A framework to integrate local information into optimal path planning,

S. Choudhury, J. D. Gammell, T. D. Barfoot, S. S. Srinivasa, and S. Scherer, “Regionally accelerated batch informed trees (RABIT*): A framework to integrate local information into optimal path planning,” in IEEE Int. Conf. Robot. Autom. IEEE, May 2016, pp. 4207–4214

work page 2016
[7]

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,” in Algorithmic Founda- tions of Robotics XI . Springer, August 2015, pp. 109–124

work page 2015
[8]

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,” in IEEE Int. Conf. Robot. Autom. , May 2016, pp. 1469– 1475

work page 2016

Show all 27 references

[9]

Kinodynamic RRT*: Asymptotically optimal motion planning for robots with linear dynamics,

D. J. Webb and J. van den Berg, “Kinodynamic RRT*: Asymptotically optimal motion planning for robots with linear dynamics,” in IEEE Int. Conf. Robot. Autom. IEEE, May 2013, pp. 5054–5061

2013
[10]

Toward asymptotically optimal motion planning for kinodynamic systems using a two-point boundary value problem solver,

C. Xie, J. van den Berg, S. Patil, and P. Abbeel, “Toward asymptotically optimal motion planning for kinodynamic systems using a two-point boundary value problem solver,” in IEEE Int. Conf. Robot. Autom. IEEE, May 2015, pp. 4187–4194

2015
[11]

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,” in Robotics Research. Springer, April 2016, pp. 649–666

2016
[12]

Generation of collision-free trajectories for a quadrocopter ﬂeet: A sequential convex programming approach,

F. Augugliaro, A. P. Schoellig, and R. D’Andrea, “Generation of collision-free trajectories for a quadrocopter ﬂeet: A sequential convex programming approach,” in IEEE/RSJ Int. Conf. Intell. Robots Syst. , October 2012, pp. 1917–1922

2012
[13]

Decoupled multiagent path planning via incremental sequential convex programming,

Y . Chen, M. Cutler, and J. P. How, “Decoupled multiagent path planning via incremental sequential convex programming,” in IEEE Int. Conf. Robot. Autom., May 2015, pp. 5954–5961

2015
[14]

Motion planning with sequential convex optimization and convex collision checking,

J. Schulman, Y . Duan, J. Ho, A. Lee, I. Awwal, H. Bradlow, J. Pan, S. Patil, K. Goldberg, and P. Abbeel, “Motion planning with sequential convex optimization and convex collision checking,” Int. J. Robot. Res. , vol. 33, no. 9, pp. 1251–1270, June 2014

2014
[15]

Online generation of collision-free trajectories for quadrotor ﬂight in unknown cluttered environments,

J. Chen, T. Liu, and S. Shen, “Online generation of collision-free trajectories for quadrotor ﬂight in unknown cluttered environments,” in IEEE Int. Conf. Robot. Autom. , May 2016, pp. 1476–1483

2016
[16]

CHOMP: Covariant hamiltonian optimization for motion planning,

M. Zucker, N. Ratliff, A. D. Dragan, M. Pivtoraiko, M. Klingensmith, C. M. Dellin, J. A. Bagnell, and S. S. Srinivasa, “CHOMP: Covariant hamiltonian optimization for motion planning,” Int. J. Robot. Res. , vol. 32, no. 9-10, pp. 1164–1193, September 2013

2013
[17]

STOMP: Stochastic trajectory optimization for motion planning,

M. Kalakrishnan, S. Chitta, E. Theodorou, P. Pastor, and S. Schaal, “STOMP: Stochastic trajectory optimization for motion planning,” in IEEE Int. Conf. Robot. Autom. IEEE, May 2011, pp. 4569–4574

2011
[18]

Continuous-time trajectory optimization for online UA V replan- ning,

H. Oleynikova, M. Burri, Z. Taylor, J. Nieto, R. Siegwart, and E. Gal- ceran, “Continuous-time trajectory optimization for online UA V replan- ning,” in IEEE/RSJ Int. Conf. Intell. Robots Syst. , October 2016, pp. 5332–5339

2016
[19]

Estimation, control, and planning for aggressive ﬂight with a small quadrotor with a single camera and IMU,

G. Loianno, C. Brunner, G. McGrath, and V . Kumar, “Estimation, control, and planning for aggressive ﬂight with a small quadrotor with a single camera and IMU,” IEEE Robot Autom. Lett. , vol. 2, no. 2, pp. 404–411, November 2017

2017
[20]

Sampling-based path planning on conﬁguration-space costmaps,

L. Jaillet, J. Cort ´es, and T. Sim ´eon, “Sampling-based path planning on conﬁguration-space costmaps,” IEEE Trans. Robot , vol. 26, no. 4, pp. 635–646, August 2010

2010
[21]

Optimal path planning in complex cost spaces with sampling-based algorithms,

D. Devaurs, T. Sim ´eon, and J. Cort ´es, “Optimal path planning in complex cost spaces with sampling-based algorithms,” IEEE Trans. Autom. Sci. Eng. , vol. 13, no. 2, pp. 415–424, April 2016

2016
[22]

Informed RRT*: Optimal sampling-based path planning focused via direct sampling of an admissible ellipsoidal heuristic,

J. D. Gammell, S. S. Srinivasa, and T. D. Barfoot, “Informed RRT*: Optimal sampling-based path planning focused via direct sampling of an admissible ellipsoidal heuristic,” in IEEE/RSJ Int. Conf. Intell. Robots Syst., September 2014, pp. 2997–3004

2014
[23]

Anytime motion planning using the RRT*,

S. Karaman, M. R. Walter, A. Perez, E. Frazzoli, and S. Teller, “Anytime motion planning using the RRT*,” in IEEE Int. Conf. Robot. Autom. IEEE, May 2011, pp. 1478–1483

2011
[24]

Neunert, C

M. Neunert, C. de Crousaz, F. Furrer, M. Kamel, F. Farshidian, R. Sieg- wart, and J. Buchli, “Fast nonlinear model predictive control for uniﬁed CAMPOS-MAC´IAS et al.: A HYBRID METHOD FOR ONLINE TRAJECTORY PLANNING OF MOBILE ROBOTS IN CLUTTERED ENVIRONMENTS 9 trajectory optimi...

2016
[25]

[Online]

Mosek ApS, The MOSEK optimization software , 2016. [Online]. Available: http://www.mosek.com/

2016
[26]

High-speed ﬂight in an ergodic forest,

S. Karaman and E. Frazzoli, “High-speed ﬂight in an ergodic forest,” in IEEE Int. Conf. Robot. Autom. , May 2012, pp. 2899–2906

2012
[27]

[Online]

Bitc raze AB, A quadcopter open platform , 2016. [Online]. Available: https://www.bitcraze.io/crazyﬂie-2/

2016

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Real-time motion planning methods for autonomous on-road driving: State-of-the-art and future research directions,

C. Katrakazas, M. Quddus, W.-H. Chen, and L. Deka, “Real-time motion planning methods for autonomous on-road driving: State-of-the-art and future research directions,” Transportation Research Part C: Emerging Technologies, vol. 60, pp. 416 – 442, November 2015

work page 2015

[2] [2]

A survey of motion planning and control techniques for self-driving urban vehicles,

B. Paden, M. Cap, S. Z. Yong, D. Yershov, and E. Frazzoli, “A survey of motion planning and control techniques for self-driving urban vehicles,” IEEE Trans. Intell. Veh., vol. 1, no. 1, pp. 33–55, March 2016

work page 2016

[3] [3]

Sampling-based algorithms for optimal motion planning,

S. Karaman and E. Frazzoli, “Sampling-based algorithms for optimal motion planning,” Int. J. Robot. Res. , vol. 30, no. 7, pp. 846–894, June 2011

work page 2011

[4] [4]

Sampling-based robot motion planning: A review,

M. Elbanhawi and M. Simic, “Sampling-based robot motion planning: A review,” IEEE Access, vol. 2, pp. 56–77, February 2014

work page 2014

[5] [5]

Batch informed trees (BIT*): Sampling-based optimal planning via the heuristically guided search of implicit random geometric graphs,

J. D. Gammell, S. S. Srinivasa, and T. D. Barfoot, “Batch informed trees (BIT*): Sampling-based optimal planning via the heuristically guided search of implicit random geometric graphs,” in IEEE Int. Conf. Robot. Autom., June 2015, pp. 3067–3074

work page 2015

[6] [6]

Regionally accelerated batch informed trees (RABIT*): A framework to integrate local information into optimal path planning,

S. Choudhury, J. D. Gammell, T. D. Barfoot, S. S. Srinivasa, and S. Scherer, “Regionally accelerated batch informed trees (RABIT*): A framework to integrate local information into optimal path planning,” in IEEE Int. Conf. Robot. Autom. IEEE, May 2016, pp. 4207–4214

work page 2016

[7] [7]

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,” in Algorithmic Founda- tions of Robotics XI . Springer, August 2015, pp. 109–124

work page 2015

[8] [8]

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,” in IEEE Int. Conf. Robot. Autom. , May 2016, pp. 1469– 1475

work page 2016