In low-temperature environments, the battery of the substation inspection robot exhibits open circuit voltage hysteresis loop distortion, resulting in severe low-temperature drift accumulation in the estimated state of charge and significant non-stationary deviations in the predicted motion energy consumption results. Therefore, this study proposes a range enhancement strategy that integrates low-temperature discharge modeling, motion energy consumption prediction and layered compensation. Firstly, a semi empirical electrochemical model is established, and an extended Kalman filter is used to estimate the state of charge of the battery online, suppressing the cumulative drift caused by low-temperature nonlinear polarization; then, combining real-time state of charge and path planning information, output the remaining endurance time prediction result in a closed form; finally, a dual layer compensation architecture is designed. The upper layer dynamically reorders inspection task points based on the endurance tension factor and adjusts the charging trigger threshold, and the lower layer designs an energy controller based on the port controlled Hamiltonian theory, optimizing joint torque distribution through injection damping and energy shaping, experiments have shown that in low-temperature environments ranging from -18 to -8℃, this strategy can complete all 8 inspection points on a single machine, with a utilization rate of 76.2% for the state of charge, which is 43.1% to 70.5% higher than existing methods. The operation time is extended by 64.8%, and the instantaneous power variation coefficient is as low as 0.11. The current sample entropy is reduced to 0.52, verifying that this measurement can achieve accurate prediction and efficient compensation of endurance under harsh low-temperature conditions.