Table 1 Summary of the key principles of hierarchical motor control⁵, with exemplar realizations in human motor control and our robotic system

Information factorization

Different information is processed by distinct sub-systems.

Factorized distribution of appropriate latent states within the generative model.

Different sensory signals are routed to different parts in the hierarchy, for example, what and where streams. These neuronal pathways can be characterized as factorized states responsible for sub-systems.

Only task-relevant sensory signals are used by individual levels, with irrelevant states hidden across levels. This speaks to an explicit factorization of sensory signals and which parts of the system have access to them.

Partial autonomy

Lower hierarchical levels can semi-autonomously produce outputs with minimum input from levels above.

The result of factorizing state space into multiple levels can independently accomplish sub-goals at a (relatively) fast temporal scale.

Semi-autonomous coordination of joint movement at lower levels (that is, brainstem and spinal cord). These operate at a faster temporal scale and do not require continuous input for higher levels.

Full autonomy and stability guaranteed at individual levels. Explicitly, we introduce stable mid-level and low-level motions for random higher-level inputs. This ensures that lower levels can independently perform fast movements.

Amortized control

Re-execute appropriate behaviours rapidly using learnt movements.

Learnt probability distributions that parameterize this generative model can be used for amortized control. That allows for habitual control based on previously learnt distributions.

The cerebellum is responsible for amortized control of deliberative and goal-directed behaviours, evoking fast habitual control for repeated actions.

The system learnt policies (that is, action-state mappings) that provide habitual control for rapidly re-executing appropriate actions.

Multi-joint coordination

Degenerate coupling of different components operating as a whole for motor control.

Result of state factorizations that introduce flexible mapping across and within each level.

Different neuronal ensembles have distinct influences, for example, the red nucleus controls movements of the arms. Much like factorized states, these neuronal ensembles come together to produce intricate movements.

The system is equipped with multiple sub-structures (or policy mappings) that are responsible for specific actuator movement. Together these come across, and within levels, to produce particular motor movements.

Temporal abstraction

Abstraction of time across hierarchical levels.

A feature of hierarchical generative models, where higher levels evolve slower than and constrain the level below.

Different levels evolve at different temporal and spatial scales, with the primary motor cortex responsible for planning (slow timescale) and spinal cord responsible for generation (fast timescale)

The three levels of the system evolve at different temporal scales, much like any hierarchical generative model. The high-level planning is at a slow timescale, mid-level stability control at medium timescale and low-level joint control at a fast timescale.