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An ethical trajectory planning algorithm for autonomous vehicles

A preprint version of the article is available at arXiv.


With the rise of artificial intelligence and automation, moral decisions that were formerly the preserve of humans are being put into the hands of algorithms. In autonomous driving, a variety of such decisions with ethical implications are made by algorithms for behaviour and trajectory planning. Therefore, here we present an ethical trajectory planning algorithm with a framework that aims at a fair distribution of risk among road users. Our implementation incorporates a combination of five ethical principles: minimization of the overall risk, priority for the worst-off, equal treatment of people, responsibility and maximum acceptable risk. To the best of our knowledge, this is the first ethical algorithm for trajectory planning of autonomous vehicles in line with the 20 recommendations from the European Union Commission expert group and with general applicability to various traffic situations. We showcase the ethical behaviour of our algorithm in selected scenarios and provide an empirical analysis of the ethical principles in 2,000 scenarios. The code used in this research is available as open-source software.

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Fig. 1: Trajectory planning based on risk distribution.
Fig. 2: Visualization of the maximum acceptable risk principle.
Fig. 3: Schematic example for the responsibility principle in the case of a rule violation.
Fig. 4: Risk distribution of the highest 100 occurring risks.
Fig. 5: Cumulated personal harm resulting from accidents during 2,000 simulated scenarios.
Fig. 6: Comparison of the ethical principles by the average deviation of the corresponding selected trajectories based on 2,000 simulated scenarios.

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Data availability

All data gathered in this research are available via figshare at This includes the evaluation files for the simulated scenarios with the three shown algorithms and a sample log file for one scenario. All remaining log files are available upon request. Source data are provided with this paper.

Code availability

The algorithm for trajectory planning40, as well as corresponding tools for analysis and visualization, are available open source at


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M.G. and F.P. received financial support from the Technical University of Munich—Institute for Ethics in Artificial Intelligence (IEAI). Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the IEAI or its partners.

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Authors and Affiliations



M.G., as the first author, initiated the idea for this paper and made essential contributions to its conception, implementation, content and experimental results. F.P. contributed to the conception and revised the paper critically. M.L. made an essential contribution to the conception of the research project. He revised the paper critically for important intellectual content. He gave final approval of the version to be published and agrees to all aspects of the work. As a guarantor, he accepts the responsibility for the overall integrity of the paper.

Corresponding author

Correspondence to Maximilian Geisslinger.

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Nature Machine Intelligence thanks Anthony Corso and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Our ethical trajectory planning algorithm in four steps.

The small orange balls symbolize trajectories that are sampled in the first step. Next, the trajectories are subjected to validity checks like in a filter screen visualized here (Step 2). Only those trajectories of the highest available validity level (here: five trajectories from ‘valid’) are assigned costs, whereas higher costs are represented with higher transparency (Step 3). In the last step, the trajectory with the lowest cost is selected.

Extended Data Fig. 2 The usage of different ethical principles for risk distribution leads to different choices.

Three exemplary and fictive scenarios which are simplified to two options (A and B) to choose from showcase the trade-offs in risk distribution regarding these principles. In every option, there are two fictive persons which are assigned a collision probability p and an estimated harm H. While option A corresponds to each of the three principles in every case, option B might be an intuitive alternative choice to many people, showing that there are good reasons to incorporate all three principles instead of relying on a single one.

Extended Data Fig. 3 Runtime analysis of the proposed algorithm.

Computation times are broken down separately by Prediction (bottom) and Planning (top) over the number of sampled trajectories. Our extensions compared to the state of the art - namely the Risk assessment and the Responsibility analysis - together require about 2 ms computing time per trajectory. The analysis was performed based on a prototype implementation without parallelization on a single thread of an Intel Core i7 (9th generation) laptop CPU.

Source data

Supplementary information

Supplementary Data 1

Evaluation files for the simulated scenarios with the three shown algorithms and a sample log file for an exemplary scenario.

Source data

Source Data Fig. 4

Statistical source data.

Source Data Fig. 5

Statistical source data.

Source Data Fig. 6

Statistical source data.

Source Data Extended Data Fig. 3

Statistical source data.

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Geisslinger, M., Poszler, F. & Lienkamp, M. An ethical trajectory planning algorithm for autonomous vehicles. Nat Mach Intell 5, 137–144 (2023).

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