cs.ROOct 24, 2026

SCET-CBF: Speed-Calibrated Soft Guidance for One-Step Dynamic Navigation

Authors: Xiaoyu Han, Dongkun Han

Organizations: University College London · Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom. · The Chinese University of Hong Kong · Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong SAR, China.

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Abstract

Control barrier functions (CBFs) support collision avoidance, yet dense dynamic encounters can leave a vehicle with no feasible command. Geometric refinements and soft constraints help preserve motion choices. Using these choices also requires accounting for the vehicle's changing turning response. For a steering-limited bicycle, braking can lower closing speed while slowing the lateral motion needed before an obstacle arrives. We propose SCET-CBF, a speed-calibrated soft guidance law for one-step dynamic navigation. A short lateral escape maneuver gives an allowable approach speed. Its speed derivative allows a quadratic program to weigh both effects of braking when choosing acceleration and steering. Soft penalties accommodate competing obstacle preferences within the input set permitted by segment and braking constraints. We derive the guidance and establish protection over each accepted motion segment, together with conditional braking invariance for a single obstacle. On 2500 paired tasks with a 60 s deadline, SCET achieves 72.8% completion, compared with 49.8% for CBF/velocity-obstacle control and 69.8% for an enhanced 1 s CBF-MPC. At 100 obstacles, SCET and the enhanced MPC complete 52.4% and 33.6% of tasks. Paired studies identify the contributions of speed feedback and early activation. Further evaluations examine the operating range under lateral acceleration limits and bounded motion and execution errors.

Figures & tables

Fig. 1: From available commands to continued passage. (a) The fan and arcs illustrate the car’s steering choices and turning-based preference. (b) Segment geometry gives the blue input domain; speed and braking retain the green set. Soft guidance selects the star within it. The orange cross is the goal-seeking input.
Fig. 2: The vehicle behind the guidance model. Wheel angle δ\delta maps to surrogate β\beta ; velocity points along θ+arctan⁡β\theta+\arctan\beta in ( 1 ).
Fig. 3: How turning response becomes a control preference. (a) Equal steering follows the same continuous-model curve, with different speeds reaching different positions after 0.5 s. (b) A tangential escape sets the proxy allowance s0s_{0} . (c) Speed moves the soft h=0h=0 boundary in relative-velocity coordinates ( d=2d=2 m, rc=0.63r^{c}=0.63 m). Braking changes both approach and allowance; the QP accounts for both changes.
Fig. 4: Local decisions build a passage through 100 moving obstacles. (a,b) Enlarged views show the car, motion and guidance. (c) The path reaches the goal at 8.05 s. Blue gives segment-safe directions and the traveled path. Magenta shows up to three nearest eligible soft rows, evaluated at the displayed state (0.22 m per m/s). Figure 5 tests full-cohort passage.
 30 s60 s
ControllerSSCET
SCET-CBF16271820067010
MAVO113412460118272
rFF-CBF adapted762764817280
DPCBF analytic4585891518933
TABLE I: One-step CBF-QP methods: 2500 paired scenarios. S: goal; C: contact before termination; E: no executable command, including failed solves; T: task timeout. Both deadlines evaluate the same trajectories.
 30 s60 s
ControllerSSCET
SCET-CBF16271820067010
MPC, H10H1011261126013740
MPC, H20+RH20+R1745174507541
TC-MPC adapted15561837646017
TABLE II: SCET and predictive control: the same 2500 scenarios, outcomes and deadlines as Table I .
Fig. 5: Passage through denser encounters. (a) One-step CBF-QP designs. (b) SCET and predictive control. Both use 500 shared scenarios per obstacle count and a 60 s deadline; rFF and TC use the common-bicycle adaptations.
Fig. 6: Speed feedback changes the selected motion. Full retains the allowance’s speed derivative; frozen suppresses it at the same allowance value for a given state. (a,b) One paired world with early activation off: positions are synchronized at 4.30 s; speed histories end at each arm’s termination. (c) Results over all 200 shared worlds. Minimum-speed occupancy is the mean per-world fraction of queries at the speed floor. The ranges cover lateral limits of 0.1g0.1g , 0.25g0.25g and 0.5g0.5g .
ControllerAccelerationVelocity jumps
SCET-CBF120/0/80/0100/0/100/0
MAVO104/0/96/052/0/148/0
MPC, H10H1049/0/151/066/0/134/0
MPC, H20+RH20+R69/0/131/0101/0/99/0
TC-MPC adaptation138/62/0/0107/91/0/2
DPCBF analytic38/0/161/121/0/179/0
TABLE III: Changed obstacle motion: 200 paired scenarios per law, 60 s. Each method uses the same one-step displacement bound in its obstacle radius. Entries are S/C/E/T.
ControllerNominal radiusWith path bound
SCET-CBF179/50/170/1167/0/232/1
MAVO85/32/283/082/14/304/0
MPC, H10H1024/16/354/615/0/377/8
MPC, H20+RH20+R23/37/335/518/0/376/6
TC-MPC adapted182/214/0/4192/199/0/9
DPCBF analytic97/5/298/099/1/300/0
TABLE IV: Execution errors: 100 shared scenarios across four actuator configurations (400 runs per arm), 60 s. Entries are S/C/E/T.
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