MongoDB 将数组元素转换为新字段

我有MongoDB集合，文档如下:

{"name": "person1", "parents": [
    {"relationship": "father", "name": "father1", "age": 40},
    {"relationship": "mother", "name": "mother1", "age": 42}
]}

{"name": "person2", "parents": [
    {"relationship": "father", "name": "father2", "age": 50},
    {"relationship": "mother", "name": "mother2", "age": 45}
]}

我正在try 将文档展平，如下所示:

{"name": "person1",  "father_name": "father1", "father_age": 40, "mother_name": "mother1", "mother_age": 42}
{"name": "person2",  "father_name": "father2", "father_age": 50, "mother_name": "mother2", "mother_age": 45}

基本上，我希望从parents个数组的每个元素(对象)中获取某些字段，并将它们作为输出文档中的新字段.我怎样才能做到这一点呢？

我编写了如下聚合管道:

[
    {
      $project: {
        _id: 0,
        name: 1,
        father_name: {
          $cond: {
            if: {
              $eq: ["$parents.relationship", "father"],
            },
            then: "$parents.name",
            else: null,
          },
        },
        father_age: {
          $cond: {
            if: {
              $eq: ["$parents.relationship", "father"],
            },
            then: "$parents.age",
            else: null,
          },
        },
        mother_name: {
          $cond: {
            if: {
              $eq: ["$parents.relationship", "mother"],
            },
            then: "$parents.name",
            else: null,
          },
        },
        mother_age: {
          $cond: {
            if: {
              $eq: ["$parents.relationship", "mother"],
            },
            then: "$parents.age",
            else: null,
          },
        },
      },
    },
  ]

但它的输出如下所示，并不像预期的那样:

{
  "name": "person1",
  "father_name": null,
  "father_age": null,
  "mother_name": null,
  "mother_age": null
}