Collaborative Robotics and Collision Avoidance in Human-Robot Shared Workspaces

Collaborative robotics blends the precision of industrial manipulators with human dexterity in a shared workspace. Safety dictates motion: power-and-force limiting and, especially, speed-and-separation monitoring (SSM) regulate robot behavior to maintain provable human–robot clearances and have shaped recent human–robot collaboration (HRC) practice. Turning these requirements into control means expressing separation and interaction constraints as bounds on position, velocity, and interaction effort, then generating trajectories and joint commands that remain feasible under sensing noise and kinematic limits. For redundant manipulators, task-priority control with null-space projection executes the primary end-effector objective while simultaneously shaping posture, respecting joint limits, and accommodating collision-avoidance biases drawn from perception. Robustness near kinematic singularities is achieved with damped least-squares (DLS) solved via singular-value decomposition (SVD), which attenuates ill-conditioned directions and regularizes the inverse kinematics in real time. Time parameterization relies on linear-segment-with-parabolic-blend (LSPB) trajectories that bound jerk and supply smooth feed-forward references compatible with high-rate control, while light Cartesian damping closes the loop on residual errors. Combined with explicit state-machine supervision that gates approach, stop, hold, repel, and resume behaviors, these elements provide a principled pathway from safety policy to executable motion for collaborative manipulation in shared workspaces. The research then develops the modeling, algorithms, and implementation needed to realize this framework end-to-end, from target acquisition and tracking with attractive or LSPB references, through collaborative operation in which motion is paused inside a risk envelope and resumed only after persistent clearance is re-established, to a fixed-TCP regime that holds the end-effector pose while the redundant chain reconfigures purely in the Jacobian null space to increase separation. Across these scenarios, repulsion acts strictly in the null space so primary objectives are preserved, posture and joint-limit biases keep configurations feasible, a gentle orientation lock prevents wrist flips near goal, and discrete-time consistency is enforced by tying trajectory sampling to the physics step and performing projection and smoothing before integration. Simulation experiments show that the unified LSPB–DLS–SVD framework acquires targets without overshoot, pauses and resumes predictably under SSM-like proximity events, and, when the TCP is fixed, keeps negligible drift while the robot reconfigures to enlarge human–robot clearance. The thesis contributes a coherent architecture for collision-aware HRC unified with a practical pipeline from human pose streams to geometric models usable by control, explicit supervisory logic that renders safety behavior interpretable, and a diagnostic methodology that exposes dexterity, proximity management, and control effort. Together these elements provide a reproducible, implementation-level account of trajectory time-parameterization, SVD-regularized DLS inverse kinematics, and null-space safety fields composed under explicit state-machine supervision to deliver robust collision avoidance for collaborative manipulation in shared workspaces.