Quadruped robots require compliance to handle unexpected external forces, such as impulsive contact forces from rough terrain, or from physical human-robot interaction. This paper presents a locomotion controller using Cartesian impedance control to coordinate tracking performance and desired compliance, along with Quadratic Programming (QP) to satisfy friction cone constraints, unilateral constraints, and torque limits. First, we resort to projected inverse-dynamics to derive an analytical control law of Cartesian impedance control for constrained and underactuated systems (typically a quadruped robot). Second, we formulate a QP to compute the optimal torques that are as close as possible to the desired values resulting from Cartesian impedance control while satisfying all of the physical constraints. When the desired motion torques lead to violation of physical constraints, the QP will result in a trade-off solution that sacrifices motion performance to ensure physical constraints. The proposed algorithm gives us more insight into the system that benefits from an analytical derivation and more efficient computation compared to hierarchical QP (HQP) controllers that typically require a solution of three QPs or more. Experiments applied on the ANYmal robot with various challenging terrains show the efficiency and performance of our controller.

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Better understanding of humans balance control is pivotal for applications such as bipedal robots and medical technologies/therapies targeting human locomotion. Despite the inverted pendulum model being popular to describe the bipedal locomotion, it does not properly capture the step-to-step transition dynamics. The major drawback has been the requirement of both feet on the ground that generates a discontinuity along the intersection of the potential energy surfaces produced by the two legs. To overcome this problem, we propose a generalised inverted pendulumbased model that can describe both single and double support phases. The full characterisation of the system potential energy allows the proposed model to drop the main limitation. This framework also enables to design optimal strategies for the transition between the two feet without the optimisation algorithms. The proposed theory has been validated by comparing the human locomotor strategies output of our planner with real-data from multiple experimental studies. The results show that our model generates trajectories consistent with human variability and performs better compared to existing well-known methods.

Minimum Jerk trajectories have been long thought to be the reference trajectories for human movements due to their impressive similarity with human movements. Nevertheless, minimum jerk trajectories are not the only choice for C ∞ (i.e., smooth) functions. For example, harmonic trajectories are smooth functions that can be superimposed to describe the evolution of physical systems. This paper analyses the possibility that motor control plans using harmonic trajectories, will be experimentally observed to have a minimum jerk likeness due to control signals being transported through the Central Nervous System (CNS) and muscle-skeletal system. We tested our theory on a 3-link arm simulation using a recently developed planner that we reformulated into a motor control architecture, inspired by the passive motion paradigm. The arm performed 100 movements, reaching for each target defined by the clock experiment. We analysed the shape of the trajectory planned in the CNS and executed in the physical simulator. We observed that even under ideal conditions (i.e., absence of delays and noise) the executed trajectories are similar to a minimum jerk trajectory; thus, supporting the thesis that the human brain might plan harmonic trajectories.

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