Temperature Observer for a Compact Multi-DOF Robotic Spherical Joint via Sensitivity-Aware LPTN and Kalman Filter

Abstract

Thermal management of robot joint motors in highly integrated multi-degree-of-freedom (multi-DOF) spherical joint structures faces challenges rooted in heat transfer inverse problems: 1) sparse measurement data caused by spatial constraints and limited sensor placement lead to severely underdetermined parameter identification problem; 2) mutually compensatory effects among complex heat transfer pathways induce multi-peak characteristics in the objective function, increasing the risk of false convergence; 3) estimating inaccessible hotspot temperatures by fusing limited experimental data with approximate models exhibits observability deficiency. To address these challenges, this paper proposes a modeling framework. First, an experimentally calibrated high-fidelity computational fluid dynamics (CFD) thermal model generates abundant simulation data, augmenting sparse measurements to enable robust initial lumped parameter thermal network (LPTN) parameter identification. Second, global sensitivity analysis via multi-factor variance decomposition identifies dominant heat transfer pathways and key parameter subsets, effectively mitigating multi-peak characteristics of the objective function. Combined with hybrid particle swarm optimization and genetic algorithm (PSO-GA), this enables robust parameter space exploration. Finally, a Kalman filter (KF)-based temperature observer is constructed that fuses model predictions with real-time measurements, ensuring observability of unmeasured states and enabling accurate reconstruction of hotspot temperatures. Experimental results demonstrate excellent estimation performance of the proposed temperature observer under dynamic conditions. Note to Practitioners—This paper is motivated by the thermal management bottlenecks in highly integrated robot joints. During heavy-duty tasks, severe space constraints prevent the installation of sufficient internal sensors to monitor critical temperature hotspots. To address this issue, we present a practical, software-based temperature tracking framework tailored for compact actuators, exoskeletons, and industrial servos. Rather than adding physical sensors, our approach combines a baseline thermal model—calibrated via early-stage simulations—with real-time readouts from just a few easily accessible surface sensors. This allows engineers to dynamically and accurately estimate internal thermal states. As a result, control systems can safely relax conservative thermal limits, pushing motors closer to their maximum performance without the risk of overheating. This framework can be extended to other multi-DOF robotic joints by re-establishing the thermal model and observer according to the joint structure, thermal coupling characteristics, operating conditions, and sensor layout. Therefore, it provides a practical and scalable workflow for thermal monitoring and temperature estimation in compact and highly integrated robotic joints.