## 3 Methods
### Negative Damping Based Swing Assist Control Strategy  
[PERSON] developed a hip exoskeleton to assist human hip movements by simplifying the human leg into an inverted pendulum model and reducing the impact of the human musculoskeletal system on hip movements to energy losses due to viscous friction and the effects of gravity. To compensate for this, [PERSON] proposed a negative damping control strategy [13].  
Therefore, the control input for an exoskeleton robot designed for gait assistance, as stated in Equation (2), consists of a negative damping torque \(\tau_{\text{ND}}\) to compensate for human viscous friction, a gravity compensation torque \(\tau_{gc}^{H}\) for the equivalent mass of the human leg, a torque to counteract the nonlinear friction \(\tau_{fc}\) of the exoskeleton robot system, and a gravity compensation torque \(\tau_{gc}\) to offset the weight of the exoskeleton robot. This is mathematically expressed as follows [13].  
\[\tau_{out}=\tau_{\text{ND}}+\tau_{gc}^{H}+\tau_{gc}+\tau_{fc} \tag{2}\]  
In this study, the control strategy of the developed KAEGO system aims to facilitate the natural flexion of the knee joint in response to the movement of the hip joint. Additionally, since the knee joint flexes naturally due to the rotational force of the hip joint and the inertial force caused by the weight of the lower limb, applying a torque \(\tau_{gc}^{H}\) to compensate for the weight of the lower limb could lead to excessive flexion of the knee joint. Therefore, in this study, the effect of the lower limb's weight is not compensated for. Consequently, the final control input for gait assistance in the KAEGO system is as follows.  
\[\tau_{out}=\tau_{\text{ND}}+\tau_{gc}+\tau_{fc} \tag{3}\]  
\[\tau_{\text{ND}}=b\omega_{k} \tag{4}\]  
Here, \(\tau_{\text{ND}}\) is calculated as the product of the knee joint's negative damping coefficient \(b\) and the rotational angular velocity \(\omega_{k}\) of the knee joint. The coefficient \(b\) represents the intrinsic viscous friction coefficient of the human lower limb, but it is impossible to estimate accurately. Moreover, the gait of hemiplegia patients not only varies greatly from individual to individual but also changes according to their condition, making it appropriate to adjust experimentally according to the state of each patient.  
The application of negative damping torque and gravity compensation torque can vary depending on the walking state. For instance, during the swing flexion state, where the movement is opposite to gravity, gravity compensation torque is needed. Conversely, in the swing extension state, where the movement is in the same direction as gravity, gravity compensation is not applied.  
The magnitude of the negative damping torque is determined based on the feedback of the knee flexion angular velocity \(\omega^{k}\), offering the advantage of responding to real-time changes in speed during walking. However, if set too high, it could lead to an abnormally large knee flexion, so its effect is limited to within a set angular range.  
Figure 5: A control block diagram representing the process of user gait intention recognition and assist mode transitions.  
Details on gravity and friction compensation methods are the same as those noted in reference [13] and thus are not described in detail in this paper.