**Rongye Shi 1,\*, Peter Steenkiste 1,2,\*and Manuela M. Veloso 3,\***


Received: 30 July 2019; Accepted: 21 September 2019; Published: 26 September 2019

**Featured Application: SC-M\* generalizes the M\* algorithm to address real-world multi-agent path planning problems in the soft-collision context, which considers the allocation of common resources requested by agents. Application examples include but are not limited to city-scale passenger routing in mass transit systems, network traffic engineering and planning for large-scale autonomous vehicles.**

**Abstract:** Multi-agent path planning (MAPP) is increasingly being used to address resource allocation problems in highly dynamic, distributed environments that involve autonomous agents. Example domains include surveillance automation, traffic control and others. Most MAPP approaches assume hard collisions, e.g., agents cannot share resources, or co-exist at the same node or edge. This assumption unnecessarily restricts the solution space and does not apply to many real-world scenarios. To mitigate this limitation, this paper introduces a more general class of MAPP problems—MAPP in a soft-collision context. In soft-collision MAPP problems, agents can share resources or co-exist in the same location at the expense of reducing the quality of the solution. Hard constraints can still be modeled by imposing a very high cost for sharing. This paper motivates and defines the soft-collision MAPP problem, and generalizes the widely-used M\* MAPP algorithm to support the concept of soft-collisions. Soft-collision M\* (SC-M\*) extends M\* by changing the definition of a collision, so paths with collisions that have a quality penalty below a given threshold are acceptable. For each candidate path, SC-M\* keeps track of the reduction in satisfaction level of each agent using a collision score, and it places agents whose collision scores exceed its threshold into a soft-collision set for reducing the score. Our evaluation shows that SC-M\* is more flexible and more scalable than M\*. It can also handle complex environments that include agents requesting different types of resources. Furthermore, we show the benefits of SC-M\* compared with several baseline algorithms in terms of path cost, success rate and run time.

**Keywords:** multi-agent systems; planning; M\* algorithm; shortest path finding; collision-free constraint; optimality and completeness
