Revealing non-analytic kinematic shifts in smooth goal-directed behaviour

How do biological agents plan and organise a smooth accurate path to shift from one smooth mode of behaviour to another as part of graceful movement that is both plastic and controlled? This paper addresses the question in conducting a novel shape analysis of approach and adjustment phases in rapid voluntary target aiming and 2-D reaching hand actions. A number of mode changing experiments are reported that investigate these actions under a range of goals and conditions. After a typically roughly aimed approach, regular projective adjustment is observed that has height and velocity kinematic profiles that are scaled copies of one another. This empirical property is encapsulated as a novel self-similar shift function. The mathematics shows that the biological shifts consist of continual deviation from their full Taylor series everywhere throughout their interval, which is a deep form of plasticity not described before. The experimental results find the same approach and adjustment strategy to occur with behavioural trajectories over the full and varied range of tested goals and conditions. The trajectory shapes have a large degree of predictability through using the shift function to handle extensive variation in the trajectories' adjustment across individual behaviours and subjects. We provide connections between the behavioural features and results and various neural studies to show how the methodology may be exploited. The conclusion is that a roughly aimed approach followed by a specific highly plastic shift adjustment can provide a regular basis for fast and accurate goal-directed motion in a simple and generalisable way.