###### Abstract  
Electrically driven legged robots have become popular in recent years. However, the development of reliable energy supply systems and effective energy management strategies for legged robots with dramatically varying power requirements still needs to be explored. This article proposes a learning-based model predictive control (MPC) energy management strategy for legged robots with battery-supercapacitor hybrid energy storage systems containing a power prediction unit and an MPC with learning-based adaptive weights. Firstly, the mathematical model of the legged robot is established, and a dual-layer long short-term memory network is constructed to predict the load power demand, providing the model and measurable disturbance for the MPC. Secondly, a multi-objective optimization objective function is established for the MPC-based energy management strategy. Three normalized terms, battery capacity loss, battery power fluctuation, and supercapacitor state-of-charge regulation, are balanced in the objective function. Finally, a deep learning algorithm is proposed to adaptively adjust the three weighting factors to meet the diverse operation conditions. Hardware-in-the-loop experimental implementations demonstrate that the proposed method can improve the kinematic performance of the legged robot by maintaining the supercapacitor state of charge at a relatively high level and reducing the battery capacity loss by 12.7% compared with the conventional MPC method. energy management strategy; electrically driven legged robot; hybrid energy storage system; learning-based model predictive control 2025 IEEEexample: accepted: 2024-113-1223-1233-1233-1233-1233-1233-1233-1233-1233-1233-1233-1233-1233-1233-1233-1233-1233-1233-1233-1233-1233-12333-12333-1233-12333-12  
efficiency and energy storage lifetime [7]. Supercapacitors (SCs) have advantages over lithium-ion batteries in their super-long service life and high power density, but they suffer from low energy density [8; 9]. A hybrid energy storage system (HESS) containing both batteries and supercapacitors can reduce the battery capacity loss and meet the challenges posed by the dramatic transient power changes of legged robots [10]. Numerous studies for electric vehicles have demonstrated the superiority of HESSs in their enhanced energy efficiency, prolonged battery life, and reduced operational cost [11; 12; 13]. Compared with electric vehicles, legged robots have more complex working conditions and dramatic load variations, presenting challenges for a HESS design. Meanwhile, the application of a HESS for legged robots has still not been fully explored. It is worth investigating the HESS application in legged robots and developing advanced energy management strategies to achieve these benefits [14]. In recent years, many researchers have been dedicated to developing effective online energy management strategies [15], which can be categorized into three types: rule based, optimization based, and learning based. The rule-based strategies typically involve deterministic power allocation rules such as logical thresholds or stochasticity rules represented by fuzzy logic [16; 17]. These strategies are simple to implement and can provide good performance in specific situations, but they heavily depend on expert experience and may not be adaptable to different situations. Learning-based energy management strategies such as deep Q-network [18], double deep Q-learning [19], and deep deterministic policy gradient integrated with adversarial imitation learning [20], which employ reinforcement learning algorithms, have gained increasing attention. Although these strategies have promising optimization capabilities, much trial-and-error training and substantial computational resources are required. Optimization-based energy management strategies have been investigated for the past decade [21], with representative dynamic programming (DP) [22] and model predictive control (MPC) [23; 24] being the most popular methods.