The article introduces PEP, a novel approach to trajectory planning for automated driving. It addresses the challenge of predicting motions of surrounding vehicles to plan the actions of the controlled ego vehicle efficiently. By combining motion prediction and trajectory planning in a joint step, PEP guarantees equivariance under roto-translations of the input space. The model generates multi-modal joint predictions for all vehicles and selects one mode as the ego plan. Additionally, an equivariant route attraction mechanism guides the ego vehicle along a high-level route without forcing it to stick to the exact path. Experimental results on the nuScenes dataset demonstrate the stability and efficacy of PEP, showcasing improvements in L2 distance at 3 seconds by 20.6% compared to state-of-the-art methods.
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