DWPP: Dynamic Window Pure Pursuit Considering Velocity and Acceleration Constraints

Fumiya Ohnishi; Masaki Takahashi

cs.ROJan 21, 2026

DWPP: Dynamic Window Pure Pursuit Considering Velocity and Acceleration Constraints

Authors: Fumiya Ohnishi, Masaki Takahashi

Abstract

Pure pursuit and its variants are widely used for mobile robot path tracking owing to their simplicity and computational efficiency. However, many conventional approaches do not explicitly account for velocity and acceleration constraints, resulting in discrepancies between commanded and actual velocities that result in overshoot and degraded tracking performance. To address this problem, this paper proposes dynamic window pure pursuit (DWPP), which fundamentally reformulates the command velocity computation process to explicitly incorporate velocity and acceleration constraints. Specifically, DWPP formulates command velocity computation in the velocity space (the $v$ - $ω$ plane) and selects the command velocity as the point within the dynamic window that is closest to the line $ω= κv$ . Experimental results demonstrate that DWPP avoids constraint-violating commands and achieves superior path-tracking accuracy compared with conventional pure pursuit methods. The proposed method has been integrated into the official Nav2 repository and is publicly available (https://github.com/ros-navigation/navigation2).

Figures & tables

Figure 1: Processing flow of conventional pure pursuit methods and the proposed method.

Figure 2: Geometric relationships between robot position, path, and lookahead position.

Panel of Figure 3 — Figure 3: Comparison of command velocity computations in the $v$ – $\omega$ space. (a) DWPP selects an executable velocity within the dynamic window closest to the line $\omega=\kappa v$ , whereas (b) conventional PP may select a velocity outside the dynamic window, which is subsequently clipped by constraints.

Panel of Figure 6 — Figure 6: Reference paths used in the experiment.

Parameter	Value
$v_{\max},v_{\min}$	0.5, 0.0 [m/s]
$a^{\mathrm{acc}}_{\max},a^{\mathrm{dcc}}_{\max}$	0.5, 0.5 [m/s 2 ]
$\omega_{\max},\omega_{\min}$	1.0, $-1.0$ [rad/s]
$\alpha^{\mathrm{acc}}_{\max},\alpha^{\mathrm{dcc}}_{\max}$	1.0, 1.0 [rad/s 2 ]
$\Delta t$	0.033 [s]
$L$	0.6 [m]

Table 1: Parameters of the PP family used in the experiment

Path	PP	APP	RPP	DWPP	MPPI
Path A	$3.3\pm 1.4$	$2.0\pm 1.1$	$1.4\pm 0.5$	$0.0\pm 0.0$	$0.1\pm 0.1$
Path B	$22.4\pm 2.7$	$13.9\pm 1.7$	$10.1\pm 0.8$	$0.0\pm 0.0$	$0.2\pm 0.1$
Path C	$55.0\pm 2.8$	$34.6\pm 0.6$	$32.1\pm 2.1$	$0.0\pm 0.0$	$0.4\pm 0.1$

Table 2: Constraint violation ratio [%] (Mean

\pm

SD)

Panel of Figure 7 — Figure 7: Experimental results in Path A: (a) paths tracked in all five trials of each controller, shown in separate panels, and (b)–(f) velocity profiles of a representative trial of each controller, where black dashed lines show the velocity limits.

Panel of Figure 8 — Figure 8: Experimental results in Path B: (a) paths tracked in all five trials of each controller, shown in separate panels, and (b)–(f) velocity profiles of a representative trial of each controller, where black dashed lines show the velocity limits.

Panel of Figure 9 — Figure 9: Experimental results in Path C: (a) paths tracked in all five trials (left: PP, APP, RPP, and DWPP, right: MPPI), and (b)–(f) velocity profiles of a representative trial of each controller, where black dashed lines show the velocity limits.

Panel of Figure 10 — Figure 10: Paths tracked in the confined corridor experiment for a representative trial (color bar from 0 to 0.5 m/s, red for fast and blue for slow).

Metric	RPP	DWPP
Constraint violation ratio [%]	$6.5\pm 1.6$	$0.0\pm 0.0$
Mean cross track error [m]	$0.03\pm 0.00$	$0.03\pm 0.00$
Max cross track error [m]	$0.11\pm 0.00$	$0.11\pm 0.01$
Travel time [s]	$24.0\pm 0.2$	$24.1\pm 0.1$

Table 6: Results of the confined corridor experiment (Mean

\pm

SD)

Panel of Figure 11 — Figure 11: Time series of a representative trial in the confined corridor experiment.

Table 7: Effect of the APP lookahead-time gain

l_{t}

on Path C.

Panel of Figure 12 — Figure 12: Effect of the APP lookahead-time gain $l_{t}$ on Path C.

Table 8: Effect of the curvature-heuristic threshold

R_{\min}

on Path C.

Panel of Figure 13 — Figure 13: Effect of the curvature-heuristic threshold $R_{\min}$ of RPP and RPP+DW on Path C.

Controller	$v_{\max}$ [m/s]	$R_{\min}$ [m]	Viol. [%]	Mean [m]	Max [m]	Time [s]
PP	0.424	–	26.0	0.10	0.46	23.2
APP	0.426	–	27.8	0.10	0.47	23.3
RPP	0.500	2.0	27.8	0.05	0.22	23.1
DWPP	0.500	0.4	0.0	0.03	0.12	23.3

Table 9: Comparison under matched travel time on Path C.

Figure 14: Effect of scaling the acceleration limits by

\gamma

on Path C.

Panel of Figure 15 — Figure 15: Velocity profiles of each controller on Path C at $\sigma_{xy}=0.05$ m (representative seed), where the black dashed lines show the velocity limits.

Table 10: Effect of localization noise on Path C. Nonzero-noise entries are mean

\pm

SD over 20 seeds, and the noise level

\sigma_{xy}

is in meters. Dashes mark settings that never reached the goal within the 120 s timeout, whose error metrics cover the truncated run.

Table 11: Effect of the lookahead distance

L

of DWPP on Path C. The

\sigma_{xy}=0.05

m entries are mean

\pm

standard deviation over 20 seeds. Dashes mark settings that never reached the goal within the 120 s timeout.

Panel of Figure 16 — Figure 16: Effect of the lookahead distance $L$ of DWPP on Path C under localization noise. The settings with $L\leq 0.3$ m at $\sigma_{xy}=0.05$ m did not reach the goal within the timeout and are excluded from the curves.

Panel of Figure 17 — Figure 17: Analysis of command velocity computation. (a) Command velocity profile; (b) and (c) dynamic window transitions at the specific time frames indicated above each plot.

Panel of Figure 18 — Figure 18: Actuator-level dynamic windows in the $v$ – $\omega$ plane.

Robot Trajectory Tracking

Robot trajectory tracking develops methods that make robots follow desired paths or motions accurately despite disturbances, uncertainty, and physical constraints.

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Lane Department of Computer Science and Electrical Engineering, West Virginia University, Morgantown, WV, USA.

Autonomous Racing RL Control Feedback Control

Open paper AskPDF arXiv

Pure Pursuit (PP) is a widely used path-tracking algorithm in autonomous vehicles due to its simplicity and real-time performance. However, its effectiveness is sensitive to the choice of lookahead distance: shorter values improve cornering but can cause instability on straights, while longer values improve smoothness but reduce accuracy in curves. We propose a hybrid control framework that integrates Proximal Policy Optimization (PPO) with the classical Pure Pursuit controller to adjust the lookahead distance dynamically during racing. The PPO agent maps vehicle speed and multi-horizon curvature features to an online lookahead command. It is trained using Stable-Baselines3 in the F1TENTH Gym simulator with a KL penalty and learning-rate decay for stability, then deployed in a ROS2 environment to guide the controller. Experiments in simulation compare the proposed method against both fixed-lookahead Pure Pursuit and an adaptive Pure Pursuit baseline. Additional real-car experiments compare the learned controller against a fixed-lookahead Pure Pursuit controller. Results show that the learned policy improves lap-time performance and repeated lap completion on unseen tracks, while also transferring zero-shot to hardware. The learned controller adapts the lookahead by increasing it on straights and reducing it in curves, demonstrating effectiveness in augmenting a classical controller by online adaptation of a single interpretable parameter. On unseen tracks, the proposed method achieved 33.16 s on Montreal and 46.05 s on Yas Marina, while tolerating more aggressive speed-profile scaling than the baselines and achieving the best lap times among the tested settings. Initial real-car experiments further support sim-to-real transfer on a 1:10-scale autonomous racing platform

Abstract

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