Autonomous grounded vehicle-based social assistance/service robot parking in an indoor environment is an exciting challenge in urban cities. There are few efficient methods for parking multi-robot/agent teams in an unknown indoor environment. The primary objective of autonomous multi-robot/agent teams is to establish synchronization between them and to stay in behavioral control when static and when in motion. In this regard, the proposed hardware-efficient algorithm addresses the parking of a trailer (follower) robot in indoor environments by a truck (leader) robot with a rendezvous approach. In the process of parking, initial rendezvous behavioral control between the truck and trailer robots is established. Next, the parking space in the environment is estimated by the truck robot, and the trailer robot parks under the supervision of the truck robot. The proposed behavioral control mechanisms were executed between heterogenous-type computational-based robots. Optimized sensors were used for traversing and the execution of the parking methods. The truck robot leads, and the trailer robot mimics the actions in the execution of path planning and parking. The truck robot was integrated with FPGA (Xilinx Zynq XC7Z020-CLG484-1), and the trailer was integrated with Arduino UNO computing devices; this heterogenous modeling is adequate in the execution of trailer parking by a truck. The hardware schemes were developed using Verilog HDL for the FPGA (truck)-based robot and Python for the Arduino (trailer)-based robot.