I have this array of JSON objects:

and I want to add a unique ID (string) to each entry, like this:

let myTree = [
    {
        text: 'Batteries',
        id: '0',
        children: [
            {
                text: 'BatteryCharge',
                id: '0-0'
            },
            {
                text: 'LiIonBattery',
                id: '0-1'
            }
        ]
    },
    {
        text: 'Supplemental',
        id: '1',
        children: [
            {
                text: 'LidarSensor',
                id: '1-0',
                children: [
                    {
                        text: 'Side',
                        id: '1-0-0'
                    },
                    {
                        text: 'Tower',
                        id: '1-0-1'
                    }
                ]
            }
        ]
    }
]

I just can't think of the right logic to achieve this. I have written this recursive function, which obviously does not achieve what I want:

function addUniqueID(tree, id=0) {
    if(typeof(tree) == "object"){
        // if the object is not an array
        if(tree.length == undefined){
            tree['id'] = String(id);
        }
        for(let key in tree) {
            addUniqueID(tree[key], id++);
        }
    }
}
addUniqueID(myTree);

How can I solve this problem?