This is one of the most common uses of present and perfect participles. The ablative of a participle and a noun/pronoun are used to create a substitute for a subordinate clause that defines the circumstances of a situation in which an action occurs.
EX: ārēus, dēspērātā pāce, ad reparandās vīrīs intendit animum- Darius, since he despaired of peace, devoted his energies to recruiting his forces (Dickinson.edu).
Ablative absolute with perfect passive participle
EX: Acceptīs litterīs, Caesar discēdit- With the letter having been received, Caesar departs (The Latin Library)
Ablative absolute with present active participle
EX: Quibus rēbus cōgnitīs Caesar apud mīlitēs cōntiōnātur- Having learned this, Cæsar makes a speech to the soldiers (Dickinson.edu)
Noun can take the place of the participle in the Ablative Absolute construction
EX: Caesare duce vincēmus. With Caesar as leader, we shall conquer (The Latin Library)