Emergency Obstacle Avoidance Maneuvers in Differential-Drive Mobile Robots

Kautik Mandve; Nilay Kant

cs.ROOct 4, 2026

Emergency Obstacle Avoidance Maneuvers in Differential-Drive Mobile Robots

Authors: Kautik Mandve, Nilay Kant

Organizations: Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, Rolla, MO 65409, USA

Abstract

Emergency obstacle avoidance requires a mobile robot to brake or change its heading within the available distance. This paper investigates the dependence of maneuver performance and odometric error on approach speed for a differential-drive robot. A footprint-clearance analysis and a normalized wheel-motion index provide a kinematic description of five braking and turning maneuvers. The principal experiment comprises 540 block-randomized trials on tile, of which 539 are retained, at commanded approach speeds of 45, 55, and 65 cm/s. An overhead camera provides an independent pose reference. When encoder, gyro, and camera heading changes are evaluated over complete motion records, the mean encoder discrepancy increases by 4.7-5.1 degrees for the two reverse-spin maneuvers between the lowest and highest speeds; the arc and brake-assisted pivot change by less than 0.4 degrees. Larger encoder discrepancy is associated with lower avoidance success after adjustment for distance, speed, maneuver, day, and turn direction. Gyro discrepancies remain approximately 3 degrees for the reverse spins. Estimated reaction distances for 90% success and their uncertainty quantify the maneuver trade-offs. The results support speed-specific empirical characterization of emergency maneuvers and distinguish encoder error from recovery motion and measurement-window mismatch.

Figures & tables

Fig. 1: Kinematic description. (a) A rectangular footprint at the initial heading and at the heading of maximum forward support. The reference point is fixed in this idealized illustration;

d

denotes initial front clearance. (b) Nominal wheel-motion indices for a common outer-wheel speed. The normalization describes wheel profiles and does not represent measured friction utilization.

Fig. 2: Illustrative M3 right turn at a 65 cm/s command. Shading denotes the commanded turn. The stored gyro summary of 70.2 degrees matches a sample 26 ms before turn completion; rotation also continues during recovery. Whole-record gyro integration follows the final camera heading more closely. Camera alignment uses cross-correlation (

r=0.992

); the population endpoint metrics do not require this alignment.

	Maneuver	$\alpha$	$K_{p},K_{d}$	Ramp (s)	Decel. fraction	Exit/top	$d$ grid (cm)
M0	Hard brake	—	$100,0$	0	—	0	2, 4, 5, 6, 8, 11
M1	Driven-inner arc	0.3	$30,2$	0.25	0.30	0.6	11, 14, 16, 18, 21, 23
M2	Brake-assisted pivot	0	$100,0$	0	0.17	0.4	7, 10, 12, 14, 17, 21
M3	Reverse spin	$-1$	$100,0$	0	0.17	0	4, 6, 8, 10, 12, 16
M4	Managed reverse spin	$-1$	$100,0$	0	0.70	0.3	4, 6, 7, 9, 11, 14

TABLE I: Maneuver parameters and principal-campaign commanded front-bumper distance grids. All turns have a nominal 90-degree encoder target.

Fig. 3: Whole-record net-heading discrepancies for the four turning maneuvers. Points are condition means; bars are 95% bootstrap intervals from resampling trials within distance cells. Each condition contains 36 trials except M4 at 65 cm/s (

n=35

). Horizontal offsets separate overlapping markers. Encoder discrepancy grows with speed for M3 and M4, whereas the integrated gyro discrepancies remain approximately constant.

Maneuver	Mean change	Interval
M1	-0.03	[-1.85, +1.80]
M2	-0.30	[-1.82, +1.22]
M3	+5.11	[+3.15, +7.07]
M4	+4.73	[+2.47, +6.97]

TABLE II: Change in mean

E_{e}

from 45 to 65 cm/s command, in degrees. Intervals are exploratory 95% bootstrap intervals.

Fig. 4: Speed-specific reaction-distance/displacement-discrepancy comparisons. Lower values are preferred. Filled markers indicate point-estimate nondominated maneuvers; hollow markers show the remaining maneuvers. Horizontal bars are 95% profile intervals for

d_{90}

and vertical bars are 95% bootstrap intervals for mean

S

. Gray lines join the point-estimate frontier and do not represent tested intermediate maneuvers. Overlapping uncertainty and the sensitivity of

S

preclude a definitive frontier-membership claim.

Maneuver	45 cm/s command	55 cm/s command	65 cm/s command
M0	3.8 [2.7, 5.9]	5.0 [4.3, 6.5]	7.6 [6.4, 9.7]
M1	17.4 [15.2, 21.7]	15.9 [14.9, 17.6]	18.8 [17.3, 22.0]
M2	9.8 [8.4, 12.0]	11.3 [9.9, 14.0]	14.1 [12.3, 17.8]
M3	5.9 [4.9, 7.6]	7.9 [6.9, 9.6]	10.7 [9.3, 13.4]
M4	7.1 [6.0, 9.4]	8.3 [7.2, 10.6]	12.8 [10.9, 16.6]

TABLE III: Estimated commanded front-bumper reaction distance

\widehat{d_{90}}

(cm), with 95% profile penalized-likelihood intervals.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Fig. 5: Observed success fractions and Firth logistic fits for every maneuver and commanded speed. Curves are drawn only over each maneuver’s tested distance range. Multiple symbols can coincide at zero or unit success. These data support the distance estimates, while the profile intervals in Table III express model-based uncertainty.

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Open paper AskPDF arXiv

Safe navigation against obstacles that can actively maneuver within bounded capabilities remains challenging: robust control barrier function methods typically treat obstacle actions as generic disturbances, while differential-game approaches are computationally expensive for online navigation. We propose an adversarially robust geometric certificate that accounts for the worst-case effect of admissible obstacle maneuvers directly in the safe-set geometry through a closed-form contraction of the certificate parameters. The construction exploits a structural property of line-of-sight (LoS) certificates: the robot and obstacle actions enter the certificate through a common state-dependent geometric gain. This gain cancels in the worst-case comparison, reducing the differential game to a direct comparison between obstacle maneuvering capability and the weaker of the robot's longitudinal and steering authorities. Instantiated on the parabolic certificate, the construction yields Adversarially Robust Dynamic Parabolic Control Barrier Functions (AR-DPCBF), for which we establish sufficient conditions for forward invariance of the contracted safe set against all admissible obstacle maneuvers under kinematic bicycle dynamics with bounded inputs. When the obstacle capability is unknown, a sliding-window estimator supplies a high-probability upper bound, allowing the guarantee to be retained with the corresponding coverage probability. We further formulate soft and buffered variants to recover feasibility in dense environments. Simulations across obstacle capabilities, densities, and capability mismatch show substantial reductions in barrier violations and collisions and demonstrate that pointwise robustification of the barrier derivative cannot substitute for contraction of its geometry.

Abstract

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