Neural Control of Movement: A Computational Perspective

AMATH 533 / CSE 529, Winter 2017, MW 4:00-5:20pm, EEB 045

Emo Todorov

CSE 434

Course Description

This graduate lecture course will provide a systematic overview of sensorimotor function on multiple levels of analysis, with emphasis on the phenomenology amenable to computational modeling. Topics include musculoskeletal mechanics, neural networks, optimal control and Bayesian inference, learning and adaptation, internal models, neural coding and decoding.

Syllabus: see introductory lecture.

Lecture slides

Lecture 1: Introduction

Lecture 2: Multi-joint kinematics and dynamics

Lecture 3: Contact dynamics

Lecture 4: Muscles

Papers for student presentation

Week 2

Featherstone and Orin (2000). Robot dynamics: Equations and algorithms. ICRA

Featherstone (2005). Efficient factorization of the joint-space inertia matrix for branch-induced kinematic trees. IJRR

Todorov (2011). A convex, smooth and invertible contact model for trajectory optimization. ICRA

Delp et al (2007). OpenSim: Open-source software to create and analyze dynamic simulations of movement. IEEE TBME

Week 3

Brown, Cheng and Loeb (1999). Measured and modeled properties of mammalian skeletal muscle. Journal of Cell Mobility Research

Garner and Pandy (2000). The obstacle-set method for representing muscle paths in musculoskeletal models. Computer Methods in Biomechanics and Biomedical Engineering

Week 4

Mussa-Ivaldi, Giszter and Bizzi (1994). Linear combinations of primitives in vertebrate motor control. PNAS

Raphael, Tsianos and Loeb (2010). Spinal-like regulator facilitates control of a two-degree-of-freedom wrist. Journal of Neuroscience

Ijspeert, Crespi, Ryczko and Cabelguen (2007). From swimming to walking with a salamander robot driven by a spinal cord model. Science

Week 5

Sergio, Hamel-Paquet and Kalaska (2005). Motor cortex neural correlates of output kinematics and kinetics during isometric-force and arm-reaching tasks. J Neurophysiol

Churchland et al (2010). Cortical preparatory activity: Representation of movement or first cog in a dynamical machine? Neuron

Kakei, Hoffman and Strick (1999). Muscle and movement representations in the primary motor cortex. Science

Kakei, Hoffman and Strick (2001). Direction of action is represented in the ventral premotor cortex. Nature Neuroscience

Todorov (2008). Recurrent neural networks trained in the presence of noise give rise to mixed muscle-movement representations.

Week 6

Graziano (2006). The organizationof behavioral repertoire in motor cortex. Annual Review of Neuroscience

Cisek and Kalaska (2010). Neural mechanisms for interacting with a world full of action choices. Annual Review of Neuroscience

Doya (2008). Modulator of decision making. Nature Neuroscience

Beck et al (2008). Probabilistic population codes for Bayesian decision making. Neuron

Week 7

Lockhart and Ting (2007). Optimal sensorimotor transformations for balance. Nature Neuroscience

Week 8

Liu and Todorov (2007). Evidence for the flexible sensorimotor strategies predicted by optimal feedback control. Journal of Neuroscience

Harris and Wolpert (1998). Signal-dependent noise determines motor planning. Nature

Srinivasan and Ruina (2006). Computer optimization of a minimal biped model discovers walking and running. Nature

Anderson and Pandy (2001). Dynamic optimization of human walking. Journal of Biomechanical Engineering

Week 9

Shadmehr and Mussa-Ivaldi (1994). Adaptive representation of dynamics during learning of a motor task. Journal of Neuroscience

Thoroughman and Shadmehr (1999). Electromyographic correlates of learning an internal model of reaching movements. Journal of Neuroscience

Sing et al (2009). Primitives for motor adaptation reflect correlated neural tuning to position and velocity. Neuron

Kording, Tenenbaum and Shadmehr (2007). The dynamics of memory as a consequence of optimal adaptation to a changing body. Nature Neuroscience

Week 10

Imamizu et al (2003). Modular organization of internal models of tools in the human cerebellum. PNAS

Thompson and Steinmetz (2009). The role of the cerebellum in classical conditioning of discrete behavioral responses. Neuroscience

Gribble et al (1998). Are complex control signals required for human arm movement? Journal of Neurophysiology

Gribble and Ostry (2000). Compensation for loads using equilibrium-point control. Experimental Brain Research

Materials from previous years

Spinal cord

Motor cortex

Higher motor areaa

Optimization and neural networks


Basal ganglia

Optimal control

Online optimization

Motor adaptation


Featherstone (2005). Spatial vector algebra: The easy way to do rigid-body dynamics. Online course

Stewart (2000). Rigid-body dynamics with friction and impact. SIAM Review

Todorov (2010). Implicit nonlinear complementarity: A new approach to contact dynamics. ICRA

Biess, Liebermann and Flash (2007). A computational model for redundant 3D pointing movements: Integration of independent spatial and temporal motor plans simplifies movement dynamics. Journal of Neuroscience

Nagengast, Braun and Wolpert (2010). Risk-sensitive opimal feedback control accounts for sensorimotor behavior under uncertainty. PLoS Computational Biology

General readings

Wolpert and Ghahramani (2000). Computational principles of movement neuroscience. Nature Neuroscience

Todorov (2002). On the role of primary motor cortex in arm movement control. Progress in Motor Control

Todorov (2004). Optimality principles in sensorimotor control. Nature Neuroscience

Scott (2004). Optimality feedback control and the neural basis of volitional motor control. Nature Neuroscience Reviews

Kording (2007). Decision theory: What "should" the nervous system do? Science

Shadmehr, Smith and Krakauer (2010). Error correction, sensory prediction, and adaptation in motor control. Annual Review of Neuroscience