Neurorobotics:From Vision to Action 62.3 The Role of the Cerebellum 1463 quire cerebellar-based controllers,the steady move of Alternative approaches use the cerebellum as an inverse robotics towards complete anthropomorphism by mim- model (see Ebadzadeh et al.[62.78]),which however icking human (hand and arm)kinematics as well as leads to increased complexity and control loop stability dynamics as closely as possible,requires the search for problems. alternative,neuromorphic control solutions. Vertebrate motor control involves the cerebral motor 62.3.2 Models of Cerebellar Control cortex,basal ganglia,thalamus,cerebellum,brain stem, and spinal cord.Motor programs,originating in the The cerebellum can be divided into two parts:the cor- cortex,are fed into the cerebellum.Combined with sen-tex and the deep nuclei.There are two systems of fibers sory information through the spinal cord,it sends motor bringing input to the both the cortex and nuclei:the commands out to the muscles via the brain stem and mossy fibers and the climbing fibers.The only out- spinal cord,which controls muscle length and joint stiff-put from the cerebellar nucleus comes from cells called ness (see Bullock and Contreras-Vidal [62.75]).The full Purkinje cells,and they project only to the cerebellar control loop is depicted in Fig.62.4 (see Schaal and nuclei,where their effect is inhibitory.This inhibition Schweighofer [62.76].for an overview of robotic ver-sculpts the output of the nuclei which(the effect varies sus brain control loops).The model in Fig.62.4 clearly from nucleus to nucleus)may act by modulating ac- resembles the well-known computed torque model and,tivity in the spinal cord,the mid-brain or the cerebral when the cerebellum is interpreted as a Smith model,cortex.We now turn to models which make explicit use it serves to cope with long delays in the control of the cellular structure of the cerebellar cortex (see Ec- loop (see Miall et al.[62.54]and van der Smagt and cles et al.[62.66]and Ito [62.79],and also Fig.62.5a). Hirzinger [62.77]).It is thus understood to incorpo- The human cerebellum has 7-14 million Purkinje cells rate a forward model of the skeletomuscular system. (PCs),each receiving about 200000 synapses.Mossy c Climbing Cortico-nuclear fibers microzone (cerebellar cortex) Parallel Parallel fibers fibers Basket cell Q Golgi Granule Granule cell cell Purkinje cell Golgi cell cell Basket cell Climbing Deep nuclei Deep hbers Mossy nucleus Mossy fibers fibers Motor cell Spinal cord b) One APG Parallel fibers d Parallel Purkinje cell State fibers encoder Granule cell Purkinje cells Granule cell Climbing Climbing Deep nucleus e fibers Mossy fibers Mossy fbers fibers One module Spinal cord Fig.62.5 (a)Major cells in the cerebellum.(b)Cells in the Marr-Albus model.The granule cells are state encoders, feeding system state,and sensor data into the PC.PC/PF synapses are adjusted using the Widrow-Hoff rule.The output of the PC are steering signals for the robotic system.(c)The APG model,using the same state encoder as in(b). (d)The MPFIM model.A single module corresponds to a group of Purkinje cells:predictor,controller,and responsibility estimator.The granule cells generate the necessary basis functions of the original informationNeurorobotics: From Vision to Action 62.3 The Role of the Cerebellum 1463 quire cerebellar-based controllers, the steady move of robotics towards complete anthropomorphism by mim￾icking human (hand and arm) kinematics as well as dynamics as closely as possible, requires the search for alternative, neuromorphic control solutions. Vertebrate motor control involves the cerebral motor cortex, basal ganglia, thalamus, cerebellum, brain stem, and spinal cord. Motor programs, originating in the cortex, are fed into the cerebellum. Combined with sen￾sory information through the spinal cord, it sends motor commands out to the muscles via the brain stem and spinal cord, which controls muscle length and joint stiff￾ness (see Bullock and Contreras-Vidal [62.75]). The full control loop is depicted in Fig. 62.4 (see Schaal and Schweighofer [62.76], for an overview of robotic ver￾sus brain control loops). The model in Fig. 62.4 clearly resembles the well-known computed torque model and, when the cerebellum is interpreted as a Smith model, it serves to cope with long delays in the control loop (see Miall et al. [62.54] and van der Smagt and Hirzinger [62.77]). It is thus understood to incorpo￾rate a forward model of the skeletomuscular system. Deep nuclei Parallel fibers Mossy fibers Granule Golgi cell cell Basket cell Cortico-nuclear microzone (cerebellar cortex) a) b) Climbing fibers Climbing fibers Parallel fibers Mossy fibers State encoder Granule cell Purkinje cell Purkinje cell Deep nucleus Deep nucleus Motor cell Parallel fibers Mossy fibers Spinal cord One APG Granule cell Golgi cell Basket cell Climbing fibers Climbing fibers Parallel fibers Mossy fibers One module Spinal cord Granule cell Purkinje cells c) d) Fig. 62.5 (a) Major cells in the cerebellum. (b) Cells in the Marr–Albus model. The granule cells are state encoders, feeding system state, and sensor data into the PC. PC/PF synapses are adjusted using the Widrow–Hoff rule. The output of the PC are steering signals for the robotic system. (c) The APG model, using the same state encoder as in (b). (d) The MPFIM model. A single module corresponds to a group of Purkinje cells: predictor, controller, and responsibility estimator. The granule cells generate the necessary basis functions of the original information Alternative approaches use the cerebellum as an inverse model (see Ebadzadeh et al. [62.78]), which however leads to increased complexity and control loop stability problems. 62.3.2 Models of Cerebellar Control The cerebellum can be divided into two parts: the cor￾tex and the deep nuclei. There are two systems of fibers bringing input to the both the cortex and nuclei: the mossy fibers and the climbing fibers. The only out￾put from the cerebellar nucleus comes from cells called Purkinje cells, and they project only to the cerebellar nuclei, where their effect is inhibitory. This inhibition sculpts the output of the nuclei which (the effect varies from nucleus to nucleus) may act by modulating ac￾tivity in the spinal cord, the mid-brain or the cerebral cortex. We now turn to models which make explicit use of the cellular structure of the cerebellar cortex (see Ec￾cles et al. [62.66] and Ito [62.79], and also Fig. 62.5a). The human cerebellum has 7–14 million Purkinje cells (PCs), each receiving about 200 000 synapses. Mossy Part G 62.3