Planning Persuasive Trajectories Based on a Leader-Follower Game Model

Chaozhe R. He; Nan Li; Yichen Dong

REVIEW 2 major objections 4 minor 16 references

Planning Persuasive Trajectories Based on a Leader-Follower Game Model

T0 review · 2 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read An autonomous vehicle can persuade a human driver to yield by planning trajectories with a leader-follower game model that predicts and shapes the driver's intentions.

desk verdict A coherent simulation study that extends the authors' LFG framework to 'persuasive' planning, but the persuasion result is only demonstrated against a synthetic human generated from the planner's own model. read the letter →

arxiv 2507.22022 v1 pith:DCCOAQCY submitted 2025-07-29 eess.SY cs.SY

Chaozhe R. He , Yichen Dong , Nan Li This is my paper

classification eess.SYcs.SY

keywords leader-followergamemodelpredictivecontrolpersuasivetrajectorieshuman-robotinteractionroleadaptationintersectionautonomousdrivingintentionshapingchanceconstraints

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 aims to show that an autonomous vehicle (AV) can do more than reactively predict a human driver's intention—it can proactively change that intention. The authors extend a leader-follower game model so that each player's role (leader or follower) can adapt over time based on Bayesian belief updates, and they embed this adaptive model in a branch model predictive control (MPC) planner. The planner evaluates two possible futures for each candidate trajectory: one where the human keeps their role, and one where they switch roles in response to the AV's actions. In a simulated unsignalized intersection, the AV is able to persuade a human-driven vehicle that initially intends to go first to yield, so the AV crosses first, while still satisfying a chance-constrained safety specification even when the human's role-switching tendency is not precisely known. If this result transfers to real driving, AVs could use such persuasive planning to improve traffic flow and assert priority safely.

What carries the argument

The central object is the adaptive leader-follower game (LFG) model extended with a role-adapting mechanism. In the original LFG, the leader assumes the follower uses a max-min strategy (an intention to yield) and optimizes its own trajectory accordingly; the follower takes a worst-case-maximizing strategy. The extension lets the role $\sigma \in \{leader, follower\}$ change: each player updates a Bayesian belief about the other's role from observed states, computes a plausible own-role distribution $\Phi$ (default: complementary to the other's likely role), and switches roles probabilistically via a $2\times 2$ transition matrix parameterized by $p_a$. The planner is a two-stage branch MPC that, for each candidate AV trajectory, predicts the human's role at a mid-horizon time $t+T_1$ from the state that trajectory produces, then evaluates cumulative reward over both resulting branches under a chance constraint. This makes the prediction closed-loop: the human's reaction to the AV's plan is part of what the AV optimizes.

What would settle it

Run a human-in-the-loop driving simulator on the same intersection scenario: if a human driver who initially commits to going first does not yield when the AV executes the persuasive MPC trajectory, or if the rate of safety-limit violations exceeds the 2% bound, the central claim fails. A cheaper check: compare real driver role-switching behavior to the transition matrix (25) with a single $p_a$; if drivers switch roles in ways the one-parameter model cannot reproduce, the predicted persuasion advantage is unsupported.

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Extended reading notes

Core claim

The central claim is that human intention in interactive traffic is not a parameter to be estimated and obeyed, but a state that can be influenced through planned action, represented by the role in a leader-follower game. The paper's adaptive LFG model lets a role change over time: each player maintains a Bayesian belief about the other's role, maps that belief to a 'plausible' complementary role for itself, and switches roles probabilistically through a transition matrix parameterized by $p_a$, the likelihood of adopting the plausible role. The robot then plans with a two-stage MPC in which the human's future role (and hence the human's predicted trajectory) is itself a function of the robot's planned trajectory. In simulations of a two-way intersection, the AV with this planner persuades a human driver that starts as a leader to become a follower and yield, reversing the baseline LFG outcome where an initial leader always crosses first; the same safety guarantee, a chance constraint with $\epsilon = 0.02$, holds across all tested levels of mismatch between the AV's assumed and the human's actual $p_a$.

Load-bearing premise

The whole persuasion mechanism presumes that real human drivers decide with the same adaptive leader-follower game model — including the Bayesian belief update, complementary role map, and one-parameter transition matrix — that the simulation uses, and no human data backs this assumption.

Editorial extensions

If this is right

An AV using the proposed planner can gain the right of way against a human-driven vehicle that starts as a leader, converting a prior deterministic loss into a persuasive win.
When the AV knows the human's switching tendency $p_a$, it succeeds in most runs for both initial human roles; when it underestimates $p_a$, the AV's planner opts not to persuade and yields priority instead, preserving safety.
Overestimating $p_a$ (believing the human is more influenceable than they are) still yields persuasion in a majority of runs across the tested range, and safety holds in all cases.
The sharp collapse in persuasion when the AV underestimates $p_a$ from 0.98 to 0.95 is tied to the 0.02 chance-constraint tolerance, showing the planner trades off persuasive advantage against probabilistic safety.
The framework generalizes the 'predict-then-plan' architecture to a closed-loop interactive one, so the AV's behavior is causally linked to the human's role change, not merely correlated.

Reading between the lines

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

If real drivers' switching decisions follow a fundamentally different mechanism (e.g., based on perceived threat or social norms rather than complementary-role logic), the persuasion guarantee may not transfer; a human-in-the-loop study is the direct test.
The single-parameter transition matrix could be extended to an online estimate of $p_a$ from observed role switches, which would reduce the risk of the sharp threshold seen at $\hat{p}_a$ around 0.95–0.98.
The same adaptive-role LFG planner could be applied to other interactive traffic settings such as highway merges or roundabouts, where altering a driver's intention to yield or merge could improve flow; the framework's complexity scales with action-set size and branch number, so receding-horizon execution would need to track the human's belief about the robot's role across MPC steps.
The paper's own simulation only randomizes the human's initial condition and treats the human model as fixed; a stronger validation would randomize the human's reward weights, noise in belief updates, and the tie-breaking rule (24), and check whether the persuasion statistics remain stable.

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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

Worth a look if you work on interaction-aware planning. The new piece here is a role-adapting leader-follower game model (Bayesian belief update plus a probabilistic role transition) and a branch MPC planner that treats the human's predicted role change as something the AV's own trajectory can steer. The authors show, in a simulated unsignalized intersection, that the AV can make the simulated HV yield more often than a fixed-role LFG baseline, with 1000-run statistics and no safety violations. The math is coherent, the simulation setup is described in enough detail to follow, and the code link is a real plus even though I didn't verify it.

The soft spot is exactly what the stress-test says: the 'human' in Section 5.1 is an LFG agent with role adaptation, using the same belief update (7), plausible-role map (14), and transition matrix (25) that the AV's predictor assumes in Section 4.1. So the persuasion result measures how well the MPC can manipulate its own model. The only divergence tested is the scalar pa vs. \hat{pa}. That is a legitimate self-consistency check, but it does not support the stronger claim that the AV 'influences human behavior' on the road. The authors are honest about this: Section 6 lists human-in-the-loop validation and a non-persuasive baseline as future work.

The parameter mismatch sensitivity is the most informative part: the AV tolerates overestimating pa but, below a threshold, it gives up and the arrival-order flips sharply. The authors even flag the threshold effect tied to epsilon. That kind of reporting is good.

Bottom line: a decent methods paper for a control/robotics audience. It deserves a serious referee, but the referee should push for a baseline against a non-persuasive planner and for either real human data or a clearly stated scope so that 'persuasion' is not oversold. I'd bring it to reading group as a maybe, and I'd cite it if I wrote about persuasive driving, with the caveat.

Referee Report

2 major / 4 minor

Summary. The paper proposes a role-adaptive leader-follower game model in which each agent holds a Bayesian belief about the other agent's role and probabilistically switches its own role according to a 'plausible' complementary-role distribution. This model is used both to predict human behavior and, inside a two-stage branch MPC, to plan trajectories that may persuade the human to yield. The framework is evaluated in a simulated two-way intersection with an AV and a human-driven vehicle, using 1000 Monte Carlo runs per condition. The results show that the AV can often cause the simulated human to yield and arrive second, with no safety violations, including under mismatches between the human's true role-change parameter pa and the AV's estimate p_hat_a.

Significance. If the behavioral predictions were independently validated, the branch-MPC formulation would be a useful contribution to interactive planning: it explicitly treats the human's role as an actionable variable, uses a tractable finite-action implementation, provides source code, and reports Monte Carlo statistics including a pa-versus-p_hat_a mismatch analysis. The internal mathematics is coherent, and the authors are candid that human-in-the-loop validation remains future work. The central limitation is that the simulated human is generated from the same adaptive LFG model that the planner assumes, so the reported 'persuasion' is currently a property of a self-consistent model rather than an established property of human drivers.

major comments (2)

[Sections 5.1–5.2] The simulated human-driven vehicle is implemented with the same adaptive LFG model—belief update (7), plausible-role map (14), and transition matrix (25)—that the AV's predictor in Section 4.1 assumes. Table 2 therefore measures how well the MPC can manipulate a synthetic human generated from the planner's own model class; the only structural divergence tested is pa versus p_hat_a. The sentence in Section 5.2, 'the proposed MPC-based interactive planning algorithm (19) enables the AV to be persuasive, influence human behavior, and gain an advantage,' overstates what the simulation supports. The manuscript should either add an evaluation with an independent human behavior model or human data, or explicitly restrict all persuasion claims to the model class of Section 3; the future-work sentence in Section 6 is not sufficient to justify the current phrasing.
[Section 5.2, Table 2] The robustness claim in the abstract ('despite uncertainties') and in Section 5.2 ('bearing uncertainties in the key parameters') is only weakly supported because persuasion collapses abruptly under small parameter error. For an HV initially in the leader role, the AV-first frequency drops from 78.9% at p_hat_a=0.98 to 0.0% at p_hat_a=0.95 when pa=1.0, and the follower rows show a similar sharp drop between p_hat_a=0.98 and p_hat_a=0.95. Safety is indeed maintained, but the persuasive advantage is not robust to a small underestimate of pa. The text acknowledges the swing, but the authors should either temper the robustness claim or add an adaptive/robust estimation scheme for pa.

minor comments (4)

[Section 5.1] The sentence 'The initial speed and position for the AV are fixed at −20 [m] and 4 [m/s]' presumably means position −20 m and speed 4 m/s; please rephrase to avoid ambiguity.
[Section 3.2, Eq. (7)] Equation (7) states that the ego player holds a belief on the constant role of the other player, while Eq. (16) lets roles change over time. Please clarify whether P(σ◦|ξt) is a belief over a time-invariant latent tendency or over the current role; if the latter, the update should include role-transition dynamics.
[Section 4.2, Eq. (19)] The chance constraint in (19) is evaluated using the predicted distribution over human roles, so the reported absence of violations is a Monte Carlo observation rather than a formal safety guarantee under model mismatch; please state this explicitly.
[Section 5.1, Eq. (25)] The row and column convention of the transition matrix in Eq. (25) is not stated; please specify whether rows correspond to the current role and columns to the next role.

Circularity Check

1 steps flagged · score 6.0 of 10

Persuasion claim reduces to manipulating a synthetic human generated by the same adaptive LFG equations the planner assumes; no independent human model or data supports the role-switching prediction.

other [Section 4.1 (Eq. 16); Section 5.1 (Eqs. 24-25); Section 5.2, Table 2]
"The robot assumes that the human behaves as an LFG model with role adaptation. ... We assume the HV uses an LFG model with the plausible role distribution Pp(σH t ) ... pa ∈ [0,1] captures the likelihood of the human to alter its role to the plausible role if different, which also capture how easy the human may be influenced."

The AV's interactive predictor (Eq. 16) computes the human's role adjustment using the same Bayesian update, plausible-role map, and transition-matrix structure (Eqs. 7, 14, 25) that the simulated HV uses to generate its actual behavior. In the LFG+MPC runs, the HV is not an independent agent; it is a realization of the exact model family the planner assumes, with pa in place of ˆpa. Therefore the reported 'persuasion' in Section 5.2—HV switching from leader to follower after the AV's planned trajectory—is the AV exploiting the model's own prescribed role-switching rule, not evidence about real human intentions. The parameter mismatch pa vs.

full rationale

The internal game-theoretic derivation is self-contained: Eqs. (4)-(6) define the leader-follower game, and Eq. (19) is a coherent chance-constrained MPC formulation. The circularity is not in the mathematics but in the evidentiary chain for the central claim that the AV can 'influence human behavior' (Section 5.2). The only tested human is generated by the same adaptive LFG model with the same transition matrix structure (Eq. 25) that the AV's predictor assumes (Eq. 16). Thus the observed role switch and priority gain are the AV controlling a synthetic agent whose response is defined by the planner's own model. The paper's self-citations for the LFG model's predictive accuracy are asserted rather than re-derived here, but the decisive issue is that the persuasion result reduces to same-model simulation rather than independent validation. Because the central empirical claim is partially circular by construction while the planning algorithm itself remains internally valid, a score of 6 is appropriate.

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

No new physical entities are introduced in this work, only a stochastic model of an existing latent variable (driver role). The framework does rely on a set of unverified modeling assumptions about human decision-making, which are the main epistemic load.

free parameters (5)

pa (human role-change willingness) = varied between 0.3 and 1.0 in Table 2; pa=1 in LFG-only
Controls probability the human switches to the complementary role; the planner's success rate depends strongly on it (Table 2 rows show AV-first percentage ranging from 87.8% to 0%).
ˆpa (AV's estimate of pa) = varied between 0.70 and 1.00
When AV underestimates pa (ˆpa < pa), persuasion fails or flips priority to HV (e.g., 0.0% AV-first for Leader, 1.00/0.95). This is a load-bearing sensitivity.
W (belief-update covariance) = not specified in text
Equation (9) defines the likelihood as N(rt|σ=ε, 0, W), but no value for W is given. The belief update, and thus all role predictions, depend on this unstated tuning parameter.
w1, w2 (reward weights) = not specified numerically in this text
The reward (23) is a weighted combination of progress, collision penalty, and effort. The balancing of these weights shapes what 'persuasive' means and is not quantified in the manuscript.
ϵ (chance constraint level) = 0.02
Safety is enforced as a chance constraint with ϵ=0.02. The authors note the large behavioral swing between ˆpa=0.98 and 0.95 is 'associated with the chance constraint level set ϵ', so results are sensitive to this choice.

assumptions (5)

domain assumption The human driver behaves as an LFG model with adaptive roles (Eqs. 5,6,12,14,24,25).
Section 4.1 states 'The robot assumes that the human behaves as an LFG model with role adaptation'. The simulation then uses exactly this model as the human. Real human behavior may deviate, and the paper provides no human-in-the-loop validation.
domain assumption The follower uses a max-min strategy and the leader optimizes against the follower's best response (Eqs. 5,6).
These strategies, inherited from Li et al. (2020), encode yielding and proceeding intentions. If real drivers do not use worst-case reasoning, the predicted actions are not meaningful.
standard math Role beliefs are updated via Bayesian inference with a zero-mean normal residual likelihood (Eqs. 7,9).
The update is standard Bayesian filtering; however, the normal covariance W is unstated and the residual definition assumes the LFG forecast is the true conditional mean.
ad hoc to paper The role transition matrix Π has the specific structure of Eq. (25), with a single parameter pa controlling switching to the 'plausible' role.
This is a designer's choice, not derived from observational data. The simulation results depend on pa and the tie-breaker in (24).
ad hoc to paper The 'plausible' role distribution Φ is complementary to the belief on the other player (Eq. 14).
The paper acknowledges 'alternative designs of Φ accounting for other considerations are also possible'. The complementary-role choice is one option and is used in all simulations.

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Cite this review

Pith. "Pith review of Planning Persuasive Trajectories Based on a Leader-Follower Game Model." pith.science (2026). https://pith.science/paper/DCCOAQCY

@misc{pith2026250722022,
  author       = {Pith},
  title        = {Pith review of: Planning Persuasive Trajectories Based on a Leader-Follower Game Model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DCCOAQCY}},
  note         = {Machine review of arXiv:2507.22022}
}

read the original abstract

We propose a framework that enables autonomous vehicles (AVs) to proactively shape the intentions and behaviors of interacting human drivers. The framework employs a leader-follower game model with an adaptive role mechanism to predict human interaction intentions and behaviors. It then utilizes a branch model predictive control (MPC) algorithm to plan the AV trajectory, persuading the human to adopt the desired intention. The proposed framework is demonstrated in an intersection scenario. Simulation results illustrate the effectiveness of the framework for generating persuasive AV trajectories despite uncertainties.

Figures

Figures reproduced from arXiv: 2507.22022 by the authors.

**Figure 1.** Closed-loop MPC-based strategy. The top branch corresponds to the prediction of human’s behavior, while the lower branch corresponds to the robot’s planned motion. The black solid branches in the human prediction are affected by the state at t. The blue dashed branches are affected by the robot’s behavior between [t, t + T1], which is also marked as a blue dashed branch, through the change of role σ H t+T1 . human … view at source ↗

**Figure 2.** Time profile comparison plots. The left column corresponds to the run when both human and AV are using the leader-follower game (LFG) to make decisions, while the right column corresponds to the run when human and AV are using LFG and MPC model (19) to make a decision. In all panels, the blue profile corresponds to a blue human-driven vehicle that is traveling northbound, while the red profile corresponds to the red… view at source ↗

**Figure 3.** Topview lapse comparison. The left column corresponds to the run when both human and AV are using the leader-follower game (LFG) model to make decisions, while the right column corresponds to the run when human and AV are using LFG and MPC model (19) to make a decision. In all frames, the blue vehicle and legend correspond to the HV, while the red vehicle corresponds to the AV, and their time profiles are shown as b… view at source ↗

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Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages

[1]

Bahram, M., Lawitzky, A., Friedrichs, J., Aeberhard, M., and Wollherr, D. (2015). A game-theoretic approach to replanning-aware interactive scene prediction and planning. IEEE Transactions on Vehicular Technology , 65(6), 3981–3992

work page 2015
[2]

and Li, N

He, C.R. and Li, N. (2024). Eco-driving accounting for interactive cut-in vehicles. In International Confer- ence on Mobility, Operations, Services and Technologies (MOST), 90–100. IEEE

work page 2024
[3]

Hwang, I., Balakrishnan, H., and Tomlin, C. (2006). State estimation for hybrid systems: applications to aircraft tracking. IEE Proceedings-Control Theory and Applica- tions, 153(5), 556–566

work page 2006
[4]

Lefkopoulos, V., Menner, M., Domahidi, A., and Zeilinger, M.N. (2020). Interaction-aware motion prediction for autonomous driving: A multiple model Kalman filtering scheme. IEEE Robotics and Automation Letters , 6(1), 80–87

work page 2020
[5]

Li, N., Oyler, D.W., Zhang, M., Yildiz, Y., Kolmanovsky, I., and Girard, A.R. (2017). Game theoretic modeling of driver and vehicle interactions for verification and validation of autonomous vehicle control systems.IEEE Transactions on Control Systems Technology , 26(5), 1782–1797

work page 2017
[6]

Li, N., Yao, Y., Kolmanovsky, I., Atkins, E., and Girard, A.R. (2020). Game-theoretic modeling of multi-vehicle interactions at uncontrolled intersections.IEEE Trans- actions on Intelligent Transportation Systems , 23(2), 1428–1442

work page 2020
[7]

Liu, K., Li, N., Tseng, H.E., Kolmanovsky, I., and Girard, A. (2022). Interaction-aware trajectory prediction and planning for autonomous vehicles in forced merge sce- narios. IEEE Transactions on Intelligent Transportation Systems, 24(1), 474–488

work page 2022
[8]

Pandya, R., Wang, Z., Nakahira, Y., and Liu, C. (2024). Towards proactive safe human-robot collaborations via data-efficient conditional behavior prediction. In In- ternational Conference on Robotics and Automation (ICRA), 12956–12963. IEEE

work page 2024

Show all 16 references

[9]

Parekh, S., Habibian, S., and Losey, D.P. (2022). RILI: Robustly influencing latent intent. In International Conference on Intelligent Robots and Systems (IROS) , 1–8. IEEE

2022
[10]

Schwarting, W., Pierson, A., Alonso-Mora, J., Karaman, S., and Rus, D. (2019). Social behavior for autonomous vehicles. Proceedings of the National Academy of Sci- ences, 116(50), 24972–24978

2019
[11]

Tian, R., Li, N., Kolmanovsky, I., Yildiz, Y., and Girard, A.R. (2020). Game-theoretic modeling of traffic in unsignalized intersection network for autonomous ve- hicle control verification and validation. IEEE Trans- actions on Intelligent Transportation Systems , 23(3), 2211–2226

2020
[12]

Tian, R., Tomizuka, M., and Sun, L. (2021). Learning hu- man rewards by inferring their latent intelligence levels in multi-agent games: A theory-of-mind approach with application to driving data. In 2021 IEEE/RSJ Inter- national Conference on Intelligent Robots and Systems (I...

2021
[13]

Wang, W., Wang, L., Zhang, C., Liu, C., Sun, L., et al. (2022). Social interactions for autonomous driving: A review and perspectives. Foundations and Trends in Robotics, 10(3-4), 198–376

2022
[14]

Velenis, E., and Wang, F.Y. (2019). Driver lane change intention inference for intelligent vehicles: Framework, survey, and challenges.IEEE Transactions on Vehicular Technology, 68(5), 4377–4390

2019
[15]

Yu, H., Tseng, H.E., and Langari, R. (2018). A human- like game theory-based controller for automatic lane changing. Transportation Research Part C: Emerging Technologies, 88, 140–158

2018
[16]

Szwabowski, S., and Coskun, S. (2019). A game theo- retic model predictive controller with aggressiveness es- timationformandatorylanechange. IEEE Transactions on Intelligent Vehicles , 5(1), 75–89

2019

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Bahram, M., Lawitzky, A., Friedrichs, J., Aeberhard, M., and Wollherr, D. (2015). A game-theoretic approach to replanning-aware interactive scene prediction and planning. IEEE Transactions on Vehicular Technology , 65(6), 3981–3992

work page 2015

[2] [2]

and Li, N

He, C.R. and Li, N. (2024). Eco-driving accounting for interactive cut-in vehicles. In International Confer- ence on Mobility, Operations, Services and Technologies (MOST), 90–100. IEEE

work page 2024

[3] [3]

Hwang, I., Balakrishnan, H., and Tomlin, C. (2006). State estimation for hybrid systems: applications to aircraft tracking. IEE Proceedings-Control Theory and Applica- tions, 153(5), 556–566

work page 2006

[4] [4]

Lefkopoulos, V., Menner, M., Domahidi, A., and Zeilinger, M.N. (2020). Interaction-aware motion prediction for autonomous driving: A multiple model Kalman filtering scheme. IEEE Robotics and Automation Letters , 6(1), 80–87

work page 2020

[5] [5]

Li, N., Oyler, D.W., Zhang, M., Yildiz, Y., Kolmanovsky, I., and Girard, A.R. (2017). Game theoretic modeling of driver and vehicle interactions for verification and validation of autonomous vehicle control systems.IEEE Transactions on Control Systems Technology , 26(5), 1782–1797

work page 2017

[6] [6]

Li, N., Yao, Y., Kolmanovsky, I., Atkins, E., and Girard, A.R. (2020). Game-theoretic modeling of multi-vehicle interactions at uncontrolled intersections.IEEE Trans- actions on Intelligent Transportation Systems , 23(2), 1428–1442

work page 2020

[7] [7]

Liu, K., Li, N., Tseng, H.E., Kolmanovsky, I., and Girard, A. (2022). Interaction-aware trajectory prediction and planning for autonomous vehicles in forced merge sce- narios. IEEE Transactions on Intelligent Transportation Systems, 24(1), 474–488

work page 2022

[8] [8]

Pandya, R., Wang, Z., Nakahira, Y., and Liu, C. (2024). Towards proactive safe human-robot collaborations via data-efficient conditional behavior prediction. In In- ternational Conference on Robotics and Automation (ICRA), 12956–12963. IEEE

work page 2024