Node.js mongoose中$lookup后如何过滤多个属性

我正在尝试获取学生的电子邮件，该学生在一门课程下提交了所有作业。首先，我要检查他们是否购买了课程。我需要过滤掉

课程

和

isSubmitted

true或false。如果我使用

$和

操作，我得到的是空数组

cond: {
     $and : {
        $eq: ["$$assignmentObj.courseId", ObjectId(id)],
        $eq: ["$$assignmentObj.isSubmitted", true],
     }
}

但是，如果我尝试按此条件进行筛选，我将获得数据，但未执行

isSubmitted

true或false筛选-

cond: {
    $eq: ["$$assignmentObj.courseId", ObjectId(id)],            
}

我已经把这个写在控制器上了-

const assignmentCount = await Assignment.find({ courseId: id }).countDocuments();

const assignmentSubmittedUser = await PurchaseHistory.aggregate([
      {
        $project: {
          userId: {
            $toObjectId: "$userId"
          },
          courseId: {
            $toObjectId: "$courseId"
          },
        }
      },
      { $match: { courseId: ObjectId(id) } },
      {
        $lookup: {
          from: 'assignmenthistories',
          localField: 'userId',
          foreignField: 'user',
          as: 'assignmentList'
        }
      },
      {
        $project:
        {
          userId: 1,
          assignmentList:
          {
            $filter:
            {
              input: "$assignmentList",
              as: "assignmentObj",
              cond: {
                $and : {
                  $eq: ["$$assignmentObj.courseId", ObjectId(id)],
                  $eq: ["$$assignmentObj.isSubmitted", true],
                }
                
              }
            }
          }
        }
      },
      {
        $lookup: {
          from: 'users',
          localField: 'userId',
          foreignField: '_id',
          as: 'userDetail'
        }
      },
      {
        $project: {
          'email': { $arrayElemAt: ["$userDetail.email", 0] },
          assignmentCount: { $size: '$assignmentList' }
        }
      },
      { $match: { assignmentCount } },

    ])

---

$和

条件应该在如下数组中{$and:[{$eq:[“$$assignmentObj.courseId”，ObjectId（id）]}，{$eq:[“$$assignmentObj.isSubmitted”，true]}