Controlling the locomotion of autonomous legged robots necessitates sophisticated techniques to address system constraints, imposing significant computational demands that hinder embedded implementation. This paper proposes a novel trajectory-tracking approach for a class of affine systems with constrained controls, tailored specifically for autonomous navigation. Leveraging an algebraic strategy initially designed for trajectory-tracking in unmanned wheeled vehicles, our methodology reformulates the approach into a streamlined optimisation problem. This reformulation ensures resulting controls adhere to the robot's actuator limits and accelerations, facilitating smoother, more energy-efficient manoeuvres. The theoretical stability of the proposed controller is established, and empirical validation is conducted through field experiments. Comparative analysis against a nonlinear model predictive controller (iNMPC) with integral mode demonstrates comparable performance, with significantly reduced computational overhead. Specifically, our controller achieves results akin to an iNMPC with a control horizon of 1 (s), sampled every 0.05 (s), showcasing its efficiency in autonomous legged robot navigation.

Effective obstacle detection and avoidance play pivotal roles in the implementation of autonomous navigation systems. While numerous authors have addressed obstacle avoidance for single unicycles and car-like vehicles, this work extends the scope to encompass generalised N-trailer vehicles, consisting of a single active segment pulling an arbitrary number of trailers. In contrast to treating obstacles as hard constraints or barrier functions, we introduce a unique approach by modelling them as soft constraints. Gaussian functions are seamlessly integrated into the objective function of the model predictive controller, preserving the convexity of the search space and significantly alleviating computational demands. Although this strategy allows regions occupied by obstacles to remain viable for navigation, we counteract this by thoughtfully designing the amplitude of the Gaussian function. This design is influenced by various components within the formulation, discouraging navigation through obstacle-occupied spaces. The effectiveness of this approach is substantiated through a series of simulated and field experiments involving a tractor pulling two trailers. These experiments showcase the method’s proficiency in navigating around obstacles while maintaining computational efficiency, thereby affirming its practical viability in real-world scenarios.

In this study, we introduce an innovative off-tracking optimisation-based framework designed for Generalised N-Trailer vehicles. The task of generating feasible references for the segments of the interconnected vehicle has historically been burdensome. This challenge becomes even more pronounced as the number of trailers increases, particularly when the quantity of trailers fluctuates during operations. Our proposed method address this complexity by autonomously generating pose references for both the tractor and each trailer of the vehicle. This is achieved through a parameterisation of the desired path and attitudes to be traversed. Notably, our approach incorporates the system's model into the optimisation process as a constraint. This guarantees that the generated reference remains within the bounds of feasibility, even when the nominal path does not. Several simulated and field experiments with a tractor pulling 2 trailers show the effectiveness of the proposed method.