In　the　dynamic　and　unstructured　environment　of　human–robot　symbiosis,　companion　robots　require　natural　human–robot　interaction　and　autonomous　intelligence　through　multimodal　information　fusion　to　achieve　effective　collaboration.　Nevertheless,　the　control　precision　and　coordination　of　the　accompanying　actions　are　not　satisfactory　in　practical　applications.　This　is　primarily　attributed　to　the　difficulties　in　the　motion　coordination　between　the　accompanying　target　and　the　mobile　robot.　This　paper　proposes　a　companion　control　strategy　based　on　the　Linear　Quadratic　Regulator　(LQR)　to　enhance　the　coordination　and　precision　of　robot　companion　tasks.　This　method　enables　the　robot　to　adapt　to　sudden　changes　in　the　companion　target＇s　motion.　Besides,　the　robot　could　smoothly　avoid　obstacles　during　the　companion　process.　Firstly,　a　human–robot　companion　interaction　model　based　on　nonholonomic　constraints　is　developed　to　determine　the　relative　position　and　orientation　between　the　robot　and　the　companion　target.　Then,　an　LQR-based　companion　controller　incorporating　behavioral　dynamics　is　introduced　to　simultaneously　avoid　obstacles　and　track　the　companion　target＇s　direction　and　velocity.　Finally,　various　simulations　and　real-world　human–robot　companion　experiments　are　conducted　to　regulate　the　relative　position,　orientation,　and　velocity　between　the　target　object　and　the　robot　platform.　Experimental　results　demonstrate　the　superiority　of　this　approach　over　conventional　control　algorithms　in　terms　of　control　distance　and　directional　errors　throughout　system　operation.　The　proposed　LQR-based　control　strategy　ensures　coordinated　and　consistent　motion　with　target　persons　in　social　companion　scenarios.　©　2024　The　Author(s)