Cooperative safe planning for multiple unmanned trucks on soft terrain in open-pit mines

The complexity of soft-terrain environments in open-pit mines poses major challenges to multi-agent reinforcement learning. Conventional purely geometric obstacle-avoidance strategies ignore the underlying vehicle–terrain interaction mechanics, while existing multi-agent reinforcement learning algorithms generally use soft penalties and exhibit environmental nonstationarity induced by joint updates, resulting in poor safety and coordination on soft-terrain roads. To address these problems, this paper proposed a reinforcement learning method incorporating physical priors to learn multi-truck cooperative planning policies that satisfied an expected cumulative risk budget and fully utilized global environmental information. The Bekker-Wong terramechanics model was incorporated into the underlying structure of a constrained Markov game to account for the bearing capacity limits and physical safety boundaries of soft terrain during policy optimization. A heterogeneous dual-stream perception network integrating multi-head self-attention and a convolutional neural network was employed to enable agents to simultaneously process high-dimensional spatial physical fields and variable-length temporal topological information from multi-vehicle interaction graphs. A sequential policy update algorithm with trust-region dual projection and dynamic priorities was designed to mitigate nonstationarity and deadlock caused by concurrent multi-vehicle operation. Experimental results showed that the proposed method achieved a maximum sinkage depth of 0.187 m and a trajectory-level threshold-exceedance probability of 4.0%. Removing dynamic priorities reduced the average return by 18.3% and the task success rate by 18.8%, while removing safety constraints significantly increased the discounted cumulative cost. These results show that the proposed method balances sinkage-risk mitigation, transport efficiency, and multi-vehicle coordination stability under an expected cumulative risk constraint.