## 3 Control Strategies for Obstacle-Aided Locomotion
### Obstacle-Aided Locomotion
Instead of using additional hardware, an alternative and low-cost sensing approach was examined in [43], where robot actuators were used as sensors to allow the system to traverse an elastically deformable channel with no need for external tactile sensors. Some researchers have focused on asymmetric pushing against obstacles. For instance, a control method with a predetermined and fixed pushing pattern was presented in [44]. In this method, the information of contact affects not only adjacent joints but also a couple of neighboring joints away from a contacting link. Furthermore, the distribution of the joint torques is empirically set asymmetrically in order to propel the snake robot forward. Later on, a more general and randomised control method that prevents the snake robot to get stuck in crowded obstacles was proposed by the same research group in [45]. When locomoting through environments with obstacles, it is also important to achieve body shape compliance for the snake robot. Some researchers have focused on shape-based control approaches, where a simple motion pattern is propagated along the snake's body and dynamically adjusted according to the surrounding obstacles. For instance, a general motion planning framework for body shape control of snake robots was presented in [46]. The applicability of this framework was demonstrated for straight line path following control, and for implementing body shape compliance in environments with obstacles. Compliance is achieved by assigning mass-spring-damper dynamics to the shape curve defining the motion of the robot. The idea of adopting a shape-based control approach to achieve compliance is particularly challenging when considering snake robots with many degrees of freedom (DOF). In fact, having many DOF is both a potential benefit and a possible disadvantage. A snake robot with a large number of DOF can better comply to and therefore better move in complex environments. Yet, possessing many degrees of freedom is only an advantage if the system is capable of coordinating them to achieve desired goals in real-time. In practice, there is a trade-off between the capability of highly articulated robots to navigate complex unstructured environments and the high computational cost of coordinating their many DOF. To facilitate the coordination of many DOF, the robot shape may be used as an important component in creating a middle layer that links high-level motion planning to low-level control for the robust locomotion of articulated systems in complex terrains. This idea was presented in [47], where shape functions were introduced as the layer of abstraction that formed the basis for creating this middle layer. In particular, these shape functions were used to capture joint-to-joint coupling and provide an intuitive set of controllable parameters that adapt the system to the environment in real-time. This approach was later extended to the definition of spatial frequency and temporal phase serpenoid shape parameters [48]. This approach provides a way to intuitively adapt the shape of highly articulated robots using joint-level torque feedback control, allowing a robot to navigate its way autonomously through unknown, irregular environment scenarios. **Remark 2**. : _Most of the previous studies highlight the fact that lateral undulation is highly dependent on the actuator torque output and environmental friction._  
Based on Remark 2, interesting approaches were discussed in [4; 49; 50]. The authors focused on how to optimally use the motor torque inputs, which result in obstacle forces suitable to achieve a user-defined desired path for a snake robot. Less importance was given to the forces generated by the environmental friction. In detail, assuming a desired snake robot trajectory and the desired link angles at the obstacles in contact, the contribution was on how to map the given trajectory to obstacle contact forces, and these forces to control inputs.