Underactuated Robotics

This lecture introduces fundamental principles of robot dynamics, deriving equations of motion using Lagrangian mechanics. It establishes the basis for model-based control strategies, covering concepts essential for analyzing complex robotic systems.

This lecture introduces the fundamental concepts of nonlinear dynamical systems, analyzing system behavior, stability criteria, and phase-space analysis relevant to underactuated robotics. Key topics include fixed points, limit cycles, and basic Lyapunov stability theory.

This lecture introduces the foundational concepts of dynamic programming within the context of optimal control for underactuated robotic systems. It covers Bellman's principle of optimality and its application to discrete-time finite-horizon problems.

This lecture extends the foundational principles of dynamic programming, focusing on advanced applications relevant to optimal control and decision-making under uncertainty. It likely covers Bellman equations and value iteration in complex state spaces.

This lecture introduces the dynamics and control challenges inherent in underactuated systems through canonical examples such as acrobots, cart-poles, and quadrotors, laying the groundwork for nonlinear control strategies.

This lecture extends dynamic programming, focusing on its application to continuous state and action spaces, drawing connections to Hamilton-Jacobi-Bellman equations and their numerical approximation. It explores value iteration and policy iteration for optimal control problems.

This lecture introduces the foundational concepts of Lyapunov stability theory for analyzing nonlinear dynamical systems. It details the construction and properties of Lyapunov functions to determine system stability without explicitly solving differential equations.

This lecture introduces the foundational concept of Lyapunov functions for analyzing stability in nonlinear control systems, focusing on methods for their computational synthesis. The session covers stability definitions, invariant set theorems, and initial approaches to constructing Lyapunov functions via convex optimization.

This lecture continues the exploration of Lyapunov function computations, focusing on advanced techniques and their application to underactuated robotic systems. It details methods for proving stability and designing controllers.

This lecture introduces the foundational concepts and mathematical formulations of trajectory optimization, focusing on direct and indirect methods for solving optimal control problems in robotics. It lays the groundwork for applying nonlinear programming techniques to dynamic systems.

This lecture, part of MIT 6.8210 (Underactuated Robotics), continues the in-depth treatment of trajectory optimization, focusing on advanced techniques and their application in complex robotic systems. It builds upon foundational concepts to address practical challenges in motion planning.

This lecture addresses the critical problem of stabilizing dynamic systems along a desired trajectory, introducing methods like Linear Quadratic Regulator (LQR) and model predictive control (MPC) for robust performance.

This lecture investigates simplified dynamic models to understand the mechanics of bipedal locomotion, focusing on concepts like the compass gait and inverted pendulum models. It analyzes stability and energy efficiency in walking.

This lecture examines trajectory optimization for systems with both continuous and discrete dynamics, crucial for tasks involving contacts and mode changes. It covers techniques for solving hybrid optimal control problems.

This session addresses the complex problem of planning and controlling robotic interactions involving contact forces and transitions. It introduces models for friction and impact, and algorithms for robust contact manipulation.

This lecture explores the control and planning challenges inherent in humanoid robotics, covering topics such as balance, whole-body control, and motion generation for complex multi-joint systems.

This lecture introduces the formalisms and solution strategies for mixed-discrete and continuous optimization problems, examining the interplay between combinatorial decision-making and continuous variable landscapes.

This session covers sampling-based motion planning algorithms like RRT and PRM, emphasizing kinodynamic constraints for systems with differential equations. It details efficient pathfinding in high-dimensional spaces.

This lecture introduces the mathematical framework for modeling systems subject to random disturbances, exploring concepts like Wiener processes and Ito calculus. It lays the groundwork for understanding noise in robotic systems.

Building on stochastic dynamics, this lecture delves into designing controllers for systems operating under uncertainty, introducing concepts like Kalman filtering and optimal stochastic control via the Hamilton-Jacobi-Bellman equation.

This lecture addresses methods for designing controllers that maintain performance despite model uncertainties and external disturbances. It explores robust control theory principles and introduces policy search algorithms for reinforcement learning.

This lecture examines control strategies that rely solely on measured outputs rather than full state information, discussing observer design and the separation principle. It details how to achieve stability and performance with incomplete state knowledge.